diff --git a/packages/edit-post/src/components/header/index.js b/packages/edit-post/src/components/header/index.js
index 3aabcf87fae1e2..6aed47542ebcfe 100644
--- a/packages/edit-post/src/components/header/index.js
+++ b/packages/edit-post/src/components/header/index.js
@@ -23,14 +23,14 @@ import { useState, useCallback } from '@wordpress/element';
  * Internal dependencies
  */
 import FullscreenModeClose from './fullscreen-mode-close';
-import MoreMenu from './more-menu';
+import PostEditorMoreMenu from './more-menu';
 import PostPublishButtonOrToggle from './post-publish-button-or-toggle';
 import MainDashboardButton from './main-dashboard-button';
 import ContextualToolbar from './contextual-toolbar';
 import { store as editPostStore } from '../../store';
 import { unlock } from '../../lock-unlock';
 
-const { DocumentTools, PostViewLink, PreviewDropdown, PinnedItems } =
+const { DocumentTools, PostViewLink, PreviewDropdown, PinnedItems, MoreMenu } =
 	unlock( editorPrivateApis );
 
 const slideY = {
@@ -152,7 +152,8 @@ function Header( { setEntitiesSavedStatesCallback, initialPost } ) {
 				{ ( isWideViewport || ! showIconLabels ) && (
 					<PinnedItems.Slot scope="core" />
 				) }
-				<MoreMenu showIconLabels={ showIconLabels } />
+				<MoreMenu />
+				<PostEditorMoreMenu />
 			</motion.div>
 		</div>
 	);
diff --git a/packages/edit-post/src/components/header/more-menu/index.js b/packages/edit-post/src/components/header/more-menu/index.js
index df67ddae775a5e..c9f1c50251ca21 100644
--- a/packages/edit-post/src/components/header/more-menu/index.js
+++ b/packages/edit-post/src/components/header/more-menu/index.js
@@ -2,62 +2,47 @@
  * WordPress dependencies
  */
 import { __ } from '@wordpress/i18n';
-import { MenuGroup, DropdownMenu } from '@wordpress/components';
 import { useViewportMatch } from '@wordpress/compose';
 import { privateApis as editorPrivateApis } from '@wordpress/editor';
-import { moreVertical } from '@wordpress/icons';
+import { PreferenceToggleMenuItem } from '@wordpress/preferences';
+import { displayShortcut } from '@wordpress/keycodes';
 
 /**
  * Internal dependencies
  */
-import PreferencesMenuItem from '../preferences-menu-item';
-import ToolsMoreMenuGroup from '../tools-more-menu-group';
-import WritingMenu from '../writing-menu';
 import { unlock } from '../../../lock-unlock';
+import ManagePatternsMenuItem from './manage-patterns-menu-item';
+import WelcomeGuideMenuItem from './welcome-guide-menu-item';
+import EditPostPreferencesModal from '../../preferences-modal';
 
-const { ModeSwitcher, ActionItem, PinnedItems } = unlock( editorPrivateApis );
+const { ToolsMoreMenuGroup, ViewMoreMenuGroup } = unlock( editorPrivateApis );
 
-const MoreMenu = ( { showIconLabels } ) => {
+const MoreMenu = () => {
 	const isLargeViewport = useViewportMatch( 'large' );
 
 	return (
-		<DropdownMenu
-			icon={ moreVertical }
-			label={ __( 'Options' ) }
-			popoverProps={ {
-				placement: 'bottom-end',
-				className: 'more-menu-dropdown__content',
-			} }
-			toggleProps={ {
-				...( showIconLabels && { variant: 'tertiary' } ),
-				tooltipPosition: 'bottom',
-				showTooltip: ! showIconLabels,
-				size: 'compact',
-			} }
-		>
-			{ ( { onClose } ) => (
-				<>
-					{ showIconLabels && ! isLargeViewport && (
-						<PinnedItems.Slot
-							className={ showIconLabels && 'show-icon-labels' }
-							scope="core"
-						/>
-					) }
-					<WritingMenu />
-					<ModeSwitcher />
-					<ActionItem.Slot
-						name="core/plugin-more-menu"
-						label={ __( 'Plugins' ) }
-						as={ MenuGroup }
-						fillProps={ { onClick: onClose } }
+		<>
+			{ isLargeViewport && (
+				<ViewMoreMenuGroup>
+					<PreferenceToggleMenuItem
+						scope="core/edit-post"
+						name="fullscreenMode"
+						label={ __( 'Fullscreen mode' ) }
+						info={ __( 'Show and hide the admin user interface' ) }
+						messageActivated={ __( 'Fullscreen mode activated' ) }
+						messageDeactivated={ __(
+							'Fullscreen mode deactivated'
+						) }
+						shortcut={ displayShortcut.secondary( 'f' ) }
 					/>
-					<ToolsMoreMenuGroup.Slot fillProps={ { onClose } } />
-					<MenuGroup>
-						<PreferencesMenuItem />
-					</MenuGroup>
-				</>
+				</ViewMoreMenuGroup>
 			) }
-		</DropdownMenu>
+			<ToolsMoreMenuGroup>
+				<ManagePatternsMenuItem />
+				<WelcomeGuideMenuItem />
+			</ToolsMoreMenuGroup>
+			<EditPostPreferencesModal />
+		</>
 	);
 };
 
diff --git a/packages/edit-post/src/components/header/more-menu/manage-patterns-menu-item.js b/packages/edit-post/src/components/header/more-menu/manage-patterns-menu-item.js
new file mode 100644
index 00000000000000..9c528214699d6f
--- /dev/null
+++ b/packages/edit-post/src/components/header/more-menu/manage-patterns-menu-item.js
@@ -0,0 +1,39 @@
+/**
+ * WordPress dependencies
+ */
+import { MenuItem } from '@wordpress/components';
+import { store as coreStore } from '@wordpress/core-data';
+import { store as editorStore } from '@wordpress/editor';
+import { useSelect } from '@wordpress/data';
+import { __ } from '@wordpress/i18n';
+import { addQueryArgs } from '@wordpress/url';
+
+function ManagePatternsMenuItem() {
+	const url = useSelect( ( select ) => {
+		const { canUser } = select( coreStore );
+		const { getEditorSettings } = select( editorStore );
+
+		const isBlockTheme = getEditorSettings().__unstableIsBlockBasedTheme;
+		const defaultUrl = addQueryArgs( 'edit.php', {
+			post_type: 'wp_block',
+		} );
+		const patternsUrl = addQueryArgs( 'site-editor.php', {
+			path: '/patterns',
+		} );
+
+		// The site editor and templates both check whether the user has
+		// edit_theme_options capabilities. We can leverage that here and not
+		// display the manage patterns link if the user can't access it.
+		return canUser( 'read', 'templates' ) && isBlockTheme
+			? patternsUrl
+			: defaultUrl;
+	}, [] );
+
+	return (
+		<MenuItem role="menuitem" href={ url }>
+			{ __( 'Manage patterns' ) }
+		</MenuItem>
+	);
+}
+
+export default ManagePatternsMenuItem;
diff --git a/packages/edit-post/src/plugins/welcome-guide-menu-item/index.js b/packages/edit-post/src/components/header/more-menu/welcome-guide-menu-item.js
similarity index 100%
rename from packages/edit-post/src/plugins/welcome-guide-menu-item/index.js
rename to packages/edit-post/src/components/header/more-menu/welcome-guide-menu-item.js
diff --git a/packages/edit-post/src/components/header/preferences-menu-item/index.js b/packages/edit-post/src/components/header/preferences-menu-item/index.js
deleted file mode 100644
index cf8db6123da117..00000000000000
--- a/packages/edit-post/src/components/header/preferences-menu-item/index.js
+++ /dev/null
@@ -1,31 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { useDispatch } from '@wordpress/data';
-import { __ } from '@wordpress/i18n';
-import { MenuItem } from '@wordpress/components';
-import { privateApis as editorPrivateApis } from '@wordpress/editor';
-
-/**
- * Internal dependencies
- */
-import { unlock } from '../../../lock-unlock';
-
-const { interfaceStore } = unlock( editorPrivateApis );
-
-/**
- * Internal dependencies
- */
-
-export default function PreferencesMenuItem() {
-	const { openModal } = useDispatch( interfaceStore );
-	return (
-		<MenuItem
-			onClick={ () => {
-				openModal( 'editor/preferences' );
-			} }
-		>
-			{ __( 'Preferences' ) }
-		</MenuItem>
-	);
-}
diff --git a/packages/edit-post/src/components/header/writing-menu/index.js b/packages/edit-post/src/components/header/writing-menu/index.js
deleted file mode 100644
index 9c369c4717e9f6..00000000000000
--- a/packages/edit-post/src/components/header/writing-menu/index.js
+++ /dev/null
@@ -1,73 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { useDispatch } from '@wordpress/data';
-import { MenuGroup } from '@wordpress/components';
-import { __, _x } from '@wordpress/i18n';
-import { useViewportMatch } from '@wordpress/compose';
-import { displayShortcut } from '@wordpress/keycodes';
-import {
-	PreferenceToggleMenuItem,
-	store as preferencesStore,
-} from '@wordpress/preferences';
-import { store as editorStore } from '@wordpress/editor';
-
-function WritingMenu() {
-	const { set: setPreference } = useDispatch( preferencesStore );
-	const { toggleDistractionFree } = useDispatch( editorStore );
-
-	const turnOffDistractionFree = () => {
-		setPreference( 'core', 'distractionFree', false );
-	};
-
-	const isLargeViewport = useViewportMatch( 'medium' );
-	if ( ! isLargeViewport ) {
-		return null;
-	}
-
-	return (
-		<MenuGroup label={ _x( 'View', 'noun' ) }>
-			<PreferenceToggleMenuItem
-				scope="core"
-				name="fixedToolbar"
-				onToggle={ turnOffDistractionFree }
-				label={ __( 'Top toolbar' ) }
-				info={ __(
-					'Access all block and document tools in a single place'
-				) }
-				messageActivated={ __( 'Top toolbar activated' ) }
-				messageDeactivated={ __( 'Top toolbar deactivated' ) }
-			/>
-			<PreferenceToggleMenuItem
-				scope="core"
-				name="distractionFree"
-				handleToggling={ false }
-				onToggle={ toggleDistractionFree }
-				label={ __( 'Distraction free' ) }
-				info={ __( 'Write with calmness' ) }
-				messageActivated={ __( 'Distraction free mode activated' ) }
-				messageDeactivated={ __( 'Distraction free mode deactivated' ) }
-				shortcut={ displayShortcut.primaryShift( '\\' ) }
-			/>
-			<PreferenceToggleMenuItem
-				scope="core"
-				name="focusMode"
-				label={ __( 'Spotlight mode' ) }
-				info={ __( 'Focus on one block at a time' ) }
-				messageActivated={ __( 'Spotlight mode activated' ) }
-				messageDeactivated={ __( 'Spotlight mode deactivated' ) }
-			/>
-			<PreferenceToggleMenuItem
-				scope="core/edit-post"
-				name="fullscreenMode"
-				label={ __( 'Fullscreen mode' ) }
-				info={ __( 'Show and hide the admin user interface' ) }
-				messageActivated={ __( 'Fullscreen mode activated' ) }
-				messageDeactivated={ __( 'Fullscreen mode deactivated' ) }
-				shortcut={ displayShortcut.secondary( 'f' ) }
-			/>
-		</MenuGroup>
-	);
-}
-
-export default WritingMenu;
diff --git a/packages/edit-post/src/components/layout/index.js b/packages/edit-post/src/components/layout/index.js
index 6169e38122a0b2..176b3512eb8a4d 100644
--- a/packages/edit-post/src/components/layout/index.js
+++ b/packages/edit-post/src/components/layout/index.js
@@ -42,7 +42,6 @@ import { privateApis as blockLibraryPrivateApis } from '@wordpress/block-library
 import TextEditor from '../text-editor';
 import VisualEditor from '../visual-editor';
 import EditPostKeyboardShortcuts from '../keyboard-shortcuts';
-import EditPostPreferencesModal from '../preferences-modal';
 import InitPatternModal from '../init-pattern-modal';
 import BrowserURL from '../browser-url';
 import Header from '../header';
@@ -361,7 +360,6 @@ function Layout( { initialPost } ) {
 					next: nextShortcut,
 				} }
 			/>
-			<EditPostPreferencesModal />
 			<WelcomeGuide />
 			<InitPatternModal />
 			<PluginArea onError={ onPluginAreaError } />
diff --git a/packages/edit-post/src/components/preferences-modal/test/index.js b/packages/edit-post/src/components/preferences-modal/test/index.js
deleted file mode 100644
index 01ac1a88fbe7d8..00000000000000
--- a/packages/edit-post/src/components/preferences-modal/test/index.js
+++ /dev/null
@@ -1,28 +0,0 @@
-/**
- * External dependencies
- */
-import { render, screen } from '@testing-library/react';
-
-/**
- * WordPress dependencies
- */
-import { useSelect } from '@wordpress/data';
-
-/**
- * Internal dependencies
- */
-import EditPostPreferencesModal from '../';
-
-// This allows us to tweak the returned value on each test.
-jest.mock( '@wordpress/data/src/components/use-select', () => jest.fn() );
-jest.mock( '@wordpress/compose/src/hooks/use-viewport-match', () => jest.fn() );
-
-describe( 'EditPostPreferencesModal', () => {
-	it( 'should not render when the modal is not active', () => {
-		useSelect.mockImplementation( () => [ false, false, false ] );
-		render( <EditPostPreferencesModal /> );
-		expect(
-			screen.queryByRole( 'dialog', { name: 'Preferences' } )
-		).not.toBeInTheDocument();
-	} );
-} );
diff --git a/packages/edit-post/src/index.js b/packages/edit-post/src/index.js
index b9555f6590d711..656fa54d87bfeb 100644
--- a/packages/edit-post/src/index.js
+++ b/packages/edit-post/src/index.js
@@ -29,7 +29,6 @@ import {
  * Internal dependencies
  */
 import './hooks';
-import './plugins';
 import Editor from './editor';
 import { unlock } from './lock-unlock';
 
diff --git a/packages/edit-post/src/plugins/copy-content-menu-item/index.js b/packages/edit-post/src/plugins/copy-content-menu-item/index.js
deleted file mode 100644
index 60bbbf9c83d6eb..00000000000000
--- a/packages/edit-post/src/plugins/copy-content-menu-item/index.js
+++ /dev/null
@@ -1,29 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { MenuItem } from '@wordpress/components';
-import { useSelect, useDispatch } from '@wordpress/data';
-import { __ } from '@wordpress/i18n';
-import { useCopyToClipboard } from '@wordpress/compose';
-import { store as noticesStore } from '@wordpress/notices';
-import { store as editorStore } from '@wordpress/editor';
-
-export default function CopyContentMenuItem() {
-	const { createNotice } = useDispatch( noticesStore );
-	const { getEditedPostAttribute } = useSelect( editorStore );
-
-	function getText() {
-		return getEditedPostAttribute( 'content' );
-	}
-
-	function onSuccess() {
-		createNotice( 'info', __( 'All content copied.' ), {
-			isDismissible: true,
-			type: 'snackbar',
-		} );
-	}
-
-	const ref = useCopyToClipboard( getText, onSuccess );
-
-	return <MenuItem ref={ ref }>{ __( 'Copy all blocks' ) }</MenuItem>;
-}
diff --git a/packages/edit-post/src/plugins/index.js b/packages/edit-post/src/plugins/index.js
deleted file mode 100644
index aa663659acbdc1..00000000000000
--- a/packages/edit-post/src/plugins/index.js
+++ /dev/null
@@ -1,85 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { MenuItem, VisuallyHidden } from '@wordpress/components';
-import { store as coreStore } from '@wordpress/core-data';
-import { store as editorStore } from '@wordpress/editor';
-import { useSelect } from '@wordpress/data';
-import { external } from '@wordpress/icons';
-import { __ } from '@wordpress/i18n';
-import { registerPlugin } from '@wordpress/plugins';
-import { addQueryArgs } from '@wordpress/url';
-
-/**
- * Internal dependencies
- */
-import CopyContentMenuItem from './copy-content-menu-item';
-import KeyboardShortcutsHelpMenuItem from './keyboard-shortcuts-help-menu-item';
-import ToolsMoreMenuGroup from '../components/header/tools-more-menu-group';
-import WelcomeGuideMenuItem from './welcome-guide-menu-item';
-
-function ManagePatternsMenuItem() {
-	const url = useSelect( ( select ) => {
-		const { canUser } = select( coreStore );
-		const { getEditorSettings } = select( editorStore );
-
-		const isBlockTheme = getEditorSettings().__unstableIsBlockBasedTheme;
-		const defaultUrl = addQueryArgs( 'edit.php', {
-			post_type: 'wp_block',
-		} );
-		const patternsUrl = addQueryArgs( 'site-editor.php', {
-			path: '/patterns',
-		} );
-
-		// The site editor and templates both check whether the user has
-		// edit_theme_options capabilities. We can leverage that here and not
-		// display the manage patterns link if the user can't access it.
-		return canUser( 'read', 'templates' ) && isBlockTheme
-			? patternsUrl
-			: defaultUrl;
-	}, [] );
-
-	return (
-		<MenuItem role="menuitem" href={ url }>
-			{ __( 'Manage patterns' ) }
-		</MenuItem>
-	);
-}
-
-registerPlugin( 'edit-post', {
-	render() {
-		return (
-			<>
-				<ToolsMoreMenuGroup>
-					{ ( { onClose } ) => (
-						<>
-							<ManagePatternsMenuItem />
-							<KeyboardShortcutsHelpMenuItem
-								onSelect={ onClose }
-							/>
-							<WelcomeGuideMenuItem />
-							<CopyContentMenuItem />
-							<MenuItem
-								role="menuitem"
-								icon={ external }
-								href={ __(
-									'https://wordpress.org/documentation/article/wordpress-block-editor/'
-								) }
-								target="_blank"
-								rel="noopener noreferrer"
-							>
-								{ __( 'Help' ) }
-								<VisuallyHidden as="span">
-									{
-										/* translators: accessibility text */
-										__( '(opens in a new tab)' )
-									}
-								</VisuallyHidden>
-							</MenuItem>
-						</>
-					) }
-				</ToolsMoreMenuGroup>
-			</>
-		);
-	},
-} );
diff --git a/packages/edit-post/src/plugins/keyboard-shortcuts-help-menu-item/index.js b/packages/edit-post/src/plugins/keyboard-shortcuts-help-menu-item/index.js
deleted file mode 100644
index e86807ac4644f4..00000000000000
--- a/packages/edit-post/src/plugins/keyboard-shortcuts-help-menu-item/index.js
+++ /dev/null
@@ -1,36 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { MenuItem } from '@wordpress/components';
-import { withDispatch } from '@wordpress/data';
-import { __ } from '@wordpress/i18n';
-import { displayShortcut } from '@wordpress/keycodes';
-import { privateApis as editorPrivateApis } from '@wordpress/editor';
-
-/**
- * Internal dependencies
- */
-import { unlock } from '../../lock-unlock';
-
-const { interfaceStore } = unlock( editorPrivateApis );
-
-export function KeyboardShortcutsHelpMenuItem( { openModal } ) {
-	return (
-		<MenuItem
-			onClick={ () => {
-				openModal( 'editor/keyboard-shortcut-help' );
-			} }
-			shortcut={ displayShortcut.access( 'h' ) }
-		>
-			{ __( 'Keyboard shortcuts' ) }
-		</MenuItem>
-	);
-}
-
-export default withDispatch( ( dispatch ) => {
-	const { openModal } = dispatch( interfaceStore );
-
-	return {
-		openModal,
-	};
-} )( KeyboardShortcutsHelpMenuItem );
diff --git a/packages/edit-site/src/components/header-edit-mode/index.js b/packages/edit-site/src/components/header-edit-mode/index.js
index 902ccb19093d89..f56e370de6438f 100644
--- a/packages/edit-site/src/components/header-edit-mode/index.js
+++ b/packages/edit-site/src/components/header-edit-mode/index.js
@@ -31,7 +31,7 @@ import {
 /**
  * Internal dependencies
  */
-import MoreMenu from './more-menu';
+import SiteEditorMoreMenuItems from './more-menu';
 import SaveButton from '../save-button';
 import DocumentTools from './document-tools';
 import { store as editSiteStore } from '../../store';
@@ -43,7 +43,7 @@ import { unlock } from '../../lock-unlock';
 import { FOCUSABLE_ENTITIES } from '../../utils/constants';
 
 const { useHasBlockToolbar } = unlock( blockEditorPrivateApis );
-const { PostViewLink, PreviewDropdown, PinnedItems } =
+const { MoreMenu, PostViewLink, PreviewDropdown, PinnedItems } =
 	unlock( editorPrivateApis );
 
 export default function HeaderEditMode() {
@@ -206,7 +206,8 @@ export default function HeaderEditMode() {
 					<PostViewLink />
 					<SaveButton size="compact" />
 					{ ! isDistractionFree && <PinnedItems.Slot scope="core" /> }
-					<MoreMenu showIconLabels={ showIconLabels } />
+					<MoreMenu />
+					<SiteEditorMoreMenuItems />
 				</motion.div>
 			</div>
 		</div>
diff --git a/packages/edit-site/src/components/header-edit-mode/more-menu/index.js b/packages/edit-site/src/components/header-edit-mode/more-menu/index.js
index 5e9577a6286321..f0df5cf57fe6f0 100644
--- a/packages/edit-site/src/components/header-edit-mode/more-menu/index.js
+++ b/packages/edit-site/src/components/header-edit-mode/more-menu/index.js
@@ -1,167 +1,30 @@
 /**
  * WordPress dependencies
  */
-import { __, _x } from '@wordpress/i18n';
-import { useSelect, useDispatch } from '@wordpress/data';
-import { displayShortcut } from '@wordpress/keycodes';
-import { external, moreVertical } from '@wordpress/icons';
-import {
-	MenuGroup,
-	MenuItem,
-	VisuallyHidden,
-	DropdownMenu,
-} from '@wordpress/components';
-import {
-	PreferenceToggleMenuItem,
-	store as preferencesStore,
-} from '@wordpress/preferences';
+import { useSelect } from '@wordpress/data';
 import { store as coreStore } from '@wordpress/core-data';
-import {
-	store as editorStore,
-	privateApis as editorPrivateApis,
-} from '@wordpress/editor';
+import { privateApis as editorPrivateApis } from '@wordpress/editor';
 
 /**
  * Internal dependencies
  */
-import ToolsMoreMenuGroup from '../tools-more-menu-group';
 import SiteExport from './site-export';
 import WelcomeGuideMenuItem from './welcome-guide-menu-item';
-import CopyContentMenuItem from './copy-content-menu-item';
 import { unlock } from '../../../lock-unlock';
 
-const { ModeSwitcher, ActionItem, interfaceStore, PreferencesModal } =
-	unlock( editorPrivateApis );
+const { ToolsMoreMenuGroup, PreferencesModal } = unlock( editorPrivateApis );
 
-export default function MoreMenu( { showIconLabels } ) {
-	const { openModal } = useDispatch( interfaceStore );
-	const { set: setPreference } = useDispatch( preferencesStore );
+export default function MoreMenu() {
 	const isBlockBasedTheme = useSelect( ( select ) => {
 		return select( coreStore ).getCurrentTheme().is_block_theme;
 	}, [] );
 
-	const { toggleDistractionFree } = useDispatch( editorStore );
-
-	const turnOffDistractionFree = () => {
-		setPreference( 'core', 'distractionFree', false );
-	};
-
 	return (
 		<>
-			<DropdownMenu
-				icon={ moreVertical }
-				label={ __( 'Options' ) }
-				popoverProps={ {
-					placement: 'bottom-end',
-					className: 'more-menu-dropdown__content',
-				} }
-				toggleProps={ {
-					showTooltip: ! showIconLabels,
-					...( showIconLabels && { variant: 'tertiary' } ),
-					tooltipPosition: 'bottom',
-					size: 'compact',
-				} }
-			>
-				{ ( { onClose } ) => (
-					<>
-						<MenuGroup label={ _x( 'View', 'noun' ) }>
-							<PreferenceToggleMenuItem
-								scope="core"
-								name="fixedToolbar"
-								onToggle={ turnOffDistractionFree }
-								label={ __( 'Top toolbar' ) }
-								info={ __(
-									'Access all block and document tools in a single place'
-								) }
-								messageActivated={ __(
-									'Top toolbar activated'
-								) }
-								messageDeactivated={ __(
-									'Top toolbar deactivated'
-								) }
-							/>
-							<PreferenceToggleMenuItem
-								scope="core"
-								name="distractionFree"
-								label={ __( 'Distraction free' ) }
-								info={ __( 'Write with calmness' ) }
-								handleToggling={ false }
-								onToggle={ toggleDistractionFree }
-								messageActivated={ __(
-									'Distraction free mode activated'
-								) }
-								messageDeactivated={ __(
-									'Distraction free mode deactivated'
-								) }
-								shortcut={ displayShortcut.primaryShift(
-									'\\'
-								) }
-							/>
-							<PreferenceToggleMenuItem
-								scope="core"
-								name="focusMode"
-								label={ __( 'Spotlight mode' ) }
-								info={ __( 'Focus on one block at a time' ) }
-								messageActivated={ __(
-									'Spotlight mode activated'
-								) }
-								messageDeactivated={ __(
-									'Spotlight mode deactivated'
-								) }
-							/>
-						</MenuGroup>
-						<ModeSwitcher />
-						<ActionItem.Slot
-							name="core/plugin-more-menu"
-							label={ __( 'Plugins' ) }
-							as={ MenuGroup }
-							fillProps={ { onClick: onClose } }
-						/>
-						<MenuGroup label={ __( 'Tools' ) }>
-							{ isBlockBasedTheme && <SiteExport /> }
-							<MenuItem
-								onClick={ () =>
-									openModal( 'editor/keyboard-shortcut-help' )
-								}
-								shortcut={ displayShortcut.access( 'h' ) }
-							>
-								{ __( 'Keyboard shortcuts' ) }
-							</MenuItem>
-							<WelcomeGuideMenuItem />
-							<CopyContentMenuItem />
-							<MenuItem
-								icon={ external }
-								role="menuitem"
-								href={ __(
-									'https://wordpress.org/documentation/article/site-editor/'
-								) }
-								target="_blank"
-								rel="noopener noreferrer"
-							>
-								{ __( 'Help' ) }
-								<VisuallyHidden as="span">
-									{
-										/* translators: accessibility text */
-										__( '(opens in a new tab)' )
-									}
-								</VisuallyHidden>
-							</MenuItem>
-							<ToolsMoreMenuGroup.Slot
-								fillProps={ { onClose } }
-							/>
-						</MenuGroup>
-						<MenuGroup>
-							<MenuItem
-								onClick={ () =>
-									openModal( 'editor/preferences' )
-								}
-							>
-								{ __( 'Preferences' ) }
-							</MenuItem>
-						</MenuGroup>
-					</>
-				) }
-			</DropdownMenu>
+			<ToolsMoreMenuGroup>
+				{ isBlockBasedTheme && <SiteExport /> }
+				<WelcomeGuideMenuItem />
+			</ToolsMoreMenuGroup>
 			<PreferencesModal />
 		</>
 	);
diff --git a/packages/edit-site/src/components/header-edit-mode/tools-more-menu-group/index.js b/packages/edit-site/src/components/header-edit-mode/tools-more-menu-group/index.js
deleted file mode 100644
index 8babbdd0c3dc71..00000000000000
--- a/packages/edit-site/src/components/header-edit-mode/tools-more-menu-group/index.js
+++ /dev/null
@@ -1,16 +0,0 @@
-/**
- * WordPress dependencies
- */
-import { createSlotFill } from '@wordpress/components';
-
-const { Fill: ToolsMoreMenuGroup, Slot } = createSlotFill(
-	'EditSiteToolsMoreMenuGroup'
-);
-
-ToolsMoreMenuGroup.Slot = ( { fillProps } ) => (
-	<Slot fillProps={ fillProps }>
-		{ ( fills ) => fills && fills.length > 0 }
-	</Slot>
-);
-
-export default ToolsMoreMenuGroup;
diff --git a/packages/edit-site/src/components/header-edit-mode/more-menu/copy-content-menu-item.js b/packages/editor/src/components/more-menu/copy-content-menu-item.js
similarity index 87%
rename from packages/edit-site/src/components/header-edit-mode/more-menu/copy-content-menu-item.js
rename to packages/editor/src/components/more-menu/copy-content-menu-item.js
index 887817692239c9..8b9de82f7ac96a 100644
--- a/packages/edit-site/src/components/header-edit-mode/more-menu/copy-content-menu-item.js
+++ b/packages/editor/src/components/more-menu/copy-content-menu-item.js
@@ -12,18 +12,18 @@ import { __unstableSerializeAndClean } from '@wordpress/blocks';
 /**
  * Internal dependencies
  */
-import { store as editSiteStore } from '../../../store';
+import { store as editorStore } from '../../store';
 
 export default function CopyContentMenuItem() {
 	const { createNotice } = useDispatch( noticesStore );
-	const { getEditedPostId, getEditedPostType } = useSelect( editSiteStore );
+	const { getCurrentPostId, getCurrentPostType } = useSelect( editorStore );
 	const { getEditedEntityRecord } = useSelect( coreStore );
 
 	function getText() {
 		const record = getEditedEntityRecord(
 			'postType',
-			getEditedPostType(),
-			getEditedPostId()
+			getCurrentPostType(),
+			getCurrentPostId()
 		);
 		if ( ! record ) {
 			return '';
diff --git a/packages/editor/src/components/more-menu/index.js b/packages/editor/src/components/more-menu/index.js
new file mode 100644
index 00000000000000..6ccc01c6ac049c
--- /dev/null
+++ b/packages/editor/src/components/more-menu/index.js
@@ -0,0 +1,158 @@
+/**
+ * WordPress dependencies
+ */
+import { __, _x } from '@wordpress/i18n';
+import { useSelect, useDispatch } from '@wordpress/data';
+import { displayShortcut } from '@wordpress/keycodes';
+import { external, moreVertical } from '@wordpress/icons';
+import {
+	MenuGroup,
+	MenuItem,
+	VisuallyHidden,
+	DropdownMenu,
+} from '@wordpress/components';
+import {
+	PreferenceToggleMenuItem,
+	store as preferencesStore,
+} from '@wordpress/preferences';
+import { store as interfaceStore, ActionItem } from '@wordpress/interface';
+
+/**
+ * Internal dependencies
+ */
+import CopyContentMenuItem from './copy-content-menu-item';
+import ModeSwitcher from '../mode-switcher';
+import ToolsMoreMenuGroup from './tools-more-menu-group';
+import ViewMoreMenuGroup from './view-more-menu-group';
+import { store as editorStore } from '../../store';
+
+export default function MoreMenu() {
+	const { openModal } = useDispatch( interfaceStore );
+	const { set: setPreference } = useDispatch( preferencesStore );
+	const { toggleDistractionFree } = useDispatch( editorStore );
+	const showIconLabels = useSelect(
+		( select ) =>
+			select( preferencesStore ).get( 'core', 'showIconLabels' ),
+		[]
+	);
+	const turnOffDistractionFree = () => {
+		setPreference( 'core', 'distractionFree', false );
+	};
+
+	return (
+		<>
+			<DropdownMenu
+				icon={ moreVertical }
+				label={ __( 'Options' ) }
+				popoverProps={ {
+					placement: 'bottom-end',
+					className: 'more-menu-dropdown__content',
+				} }
+				toggleProps={ {
+					showTooltip: ! showIconLabels,
+					...( showIconLabels && { variant: 'tertiary' } ),
+					tooltipPosition: 'bottom',
+					size: 'compact',
+				} }
+			>
+				{ ( { onClose } ) => (
+					<>
+						<MenuGroup label={ _x( 'View', 'noun' ) }>
+							<PreferenceToggleMenuItem
+								scope="core"
+								name="fixedToolbar"
+								onToggle={ turnOffDistractionFree }
+								label={ __( 'Top toolbar' ) }
+								info={ __(
+									'Access all block and document tools in a single place'
+								) }
+								messageActivated={ __(
+									'Top toolbar activated'
+								) }
+								messageDeactivated={ __(
+									'Top toolbar deactivated'
+								) }
+							/>
+							<PreferenceToggleMenuItem
+								scope="core"
+								name="distractionFree"
+								label={ __( 'Distraction free' ) }
+								info={ __( 'Write with calmness' ) }
+								handleToggling={ false }
+								onToggle={ toggleDistractionFree }
+								messageActivated={ __(
+									'Distraction free mode activated'
+								) }
+								messageDeactivated={ __(
+									'Distraction free mode deactivated'
+								) }
+								shortcut={ displayShortcut.primaryShift(
+									'\\'
+								) }
+							/>
+							<PreferenceToggleMenuItem
+								scope="core"
+								name="focusMode"
+								label={ __( 'Spotlight mode' ) }
+								info={ __( 'Focus on one block at a time' ) }
+								messageActivated={ __(
+									'Spotlight mode activated'
+								) }
+								messageDeactivated={ __(
+									'Spotlight mode deactivated'
+								) }
+							/>
+							<ViewMoreMenuGroup.Slot fillProps={ { onClose } } />
+						</MenuGroup>
+						<ModeSwitcher />
+						<ActionItem.Slot
+							name="core/plugin-more-menu"
+							label={ __( 'Plugins' ) }
+							as={ MenuGroup }
+							fillProps={ { onClick: onClose } }
+						/>
+						<MenuGroup label={ __( 'Tools' ) }>
+							<MenuItem
+								onClick={ () =>
+									openModal( 'editor/keyboard-shortcut-help' )
+								}
+								shortcut={ displayShortcut.access( 'h' ) }
+							>
+								{ __( 'Keyboard shortcuts' ) }
+							</MenuItem>
+							<CopyContentMenuItem />
+							<MenuItem
+								icon={ external }
+								href={ __(
+									'https://wordpress.org/documentation/article/wordpress-block-editor/'
+								) }
+								target="_blank"
+								rel="noopener noreferrer"
+							>
+								{ __( 'Help' ) }
+								<VisuallyHidden as="span">
+									{
+										/* translators: accessibility text */
+										__( '(opens in a new tab)' )
+									}
+								</VisuallyHidden>
+							</MenuItem>
+							<ToolsMoreMenuGroup.Slot
+								fillProps={ { onClose } }
+							/>
+						</MenuGroup>
+						<MenuGroup>
+							<MenuItem
+								onClick={ () =>
+									openModal( 'editor/preferences' )
+								}
+							>
+								{ __( 'Preferences' ) }
+							</MenuItem>
+						</MenuGroup>
+					</>
+				) }
+			</DropdownMenu>
+		</>
+	);
+}
diff --git a/packages/editor/src/components/more-menu/tools-more-menu-group.js b/packages/editor/src/components/more-menu/tools-more-menu-group.js
new file mode 100644
index 00000000000000..7dec9d9d490d86
--- /dev/null
+++ b/packages/editor/src/components/more-menu/tools-more-menu-group.js
@@ -0,0 +1,11 @@
+/**
+ * WordPress dependencies
+ */
+import { createSlotFill } from '@wordpress/components';
+
+const { Fill: ToolsMoreMenuGroup, Slot } =
+	createSlotFill( 'ToolsMoreMenuGroup' );
+
+ToolsMoreMenuGroup.Slot = ( { fillProps } ) => <Slot fillProps={ fillProps } />;
+
+export default ToolsMoreMenuGroup;
diff --git a/packages/editor/src/components/more-menu/view-more-menu-group.js b/packages/editor/src/components/more-menu/view-more-menu-group.js
new file mode 100644
index 00000000000000..23e2cf82d82c6d
--- /dev/null
+++ b/packages/editor/src/components/more-menu/view-more-menu-group.js
@@ -0,0 +1,13 @@
+/**
+ * WordPress dependencies
+ */
+import { createSlotFill } from '@wordpress/components';
+import { Platform } from '@wordpress/element';
+
+const { Fill: ViewMoreMenuGroup, Slot } = createSlotFill(
+	Platform.OS === 'web' ? Symbol( 'ViewMoreMenuGroup' ) : 'ViewMoreMenuGroup'
+);
+
+ViewMoreMenuGroup.Slot = ( { fillProps } ) => <Slot fillProps={ fillProps } />;
+
+export default ViewMoreMenuGroup;
diff --git a/packages/editor/src/private-apis.js b/packages/editor/src/private-apis.js
index bff79cc034f1a7..aae3762794b4d6 100644
--- a/packages/editor/src/private-apis.js
+++ b/packages/editor/src/private-apis.js
@@ -15,7 +15,7 @@ import useBlockEditorSettings from './components/provider/use-block-editor-setti
 import DocumentTools from './components/document-tools';
 import InserterSidebar from './components/inserter-sidebar';
 import ListViewSidebar from './components/list-view-sidebar';
-import ModeSwitcher from './components/mode-switcher';
+import MoreMenu from './components/more-menu';
 import PatternOverridesPanel from './components/pattern-overrides-panel';
 import PluginPostExcerpt from './components/post-excerpt/plugin';
 import PostPanelRow from './components/post-panel-row';
@@ -26,6 +26,8 @@ import PostActions from './components/post-actions';
 import { usePostActions } from './components/post-actions/actions';
 import PostCardPanel from './components/post-card-panel';
 import PostStatus from './components/post-status';
+import ToolsMoreMenuGroup from './components/more-menu/tools-more-menu-group';
+import ViewMoreMenuGroup from './components/more-menu/view-more-menu-group';
 
 const { store: interfaceStore, ...remainingInterfaceApis } = interfaceApis;
 
@@ -37,7 +39,7 @@ lock( privateApis, {
 	EntitiesSavedStatesExtensible,
 	InserterSidebar,
 	ListViewSidebar,
-	ModeSwitcher,
+	MoreMenu,
 	PatternOverridesPanel,
 	PluginPostExcerpt,
 	PostActions,
@@ -48,6 +50,8 @@ lock( privateApis, {
 	usePostActions,
 	PostCardPanel,
 	PostStatus,
+	ToolsMoreMenuGroup,
+	ViewMoreMenuGroup,
 
 	// This is a temporary private API while we're updating the site editor to use EditorProvider.
 	useAutoSwitchEditorSidebars,