Add option to keep ```MenuAnchor``` open after ```MenuItem``` tap (#123723)

Add option to keep ```MenuAnchor``` open after ```MenuItem``` tap

packages/flutter/lib/src/material/menu_anchor.dart

@@ -810,6 +810,7 @@ class MenuItemButton extends StatefulWidget {
     this.clipBehavior = Clip.none,
     this.leadingIcon,
     this.trailingIcon,
+    this.closeOnActivate = true,
     required this.child,
   });
 
@@ -871,6 +872,14 @@ class MenuItemButton extends StatefulWidget {
   /// An optional icon to display after the [child] label.
   final Widget? trailingIcon;
 
+  /// {@template flutter.material.menu_anchor.closeOnActivate}
+  /// Determines if the menu will be closed when a [MenuItemButton]
+  /// is pressed.
+  ///
+  /// Defaults to true.
+  /// {@endtemplate}
+  final bool closeOnActivate;
+
   /// The widget displayed in the center of this button.
   ///
   /// Typically this is the button's label, using a [Text] widget.
@@ -1089,7 +1098,9 @@ class _MenuItemButtonState extends State<MenuItemButton> {
   void _handleSelect() {
     assert(_debugMenuInfo('Selected ${widget.child} menu'));
     widget.onPressed?.call();
-    _MenuAnchorState._maybeOf(context)?._root._close();
+    if (widget.closeOnActivate) {
+      _MenuAnchorState._maybeOf(context)?._root._close();
+    }
   }
 
   void _createInternalFocusNodeIfNeeded() {
@@ -1140,6 +1151,7 @@ class CheckboxMenuButton extends StatelessWidget {
     this.statesController,
     this.clipBehavior = Clip.none,
     this.trailingIcon,
+    this.closeOnActivate = true,
     required this.child,
   });
 
@@ -1242,6 +1254,9 @@ class CheckboxMenuButton extends StatelessWidget {
   /// An optional icon to display after the [child] label.
   final Widget? trailingIcon;
 
+  /// {@macro flutter.material.menu_anchor.closeOnActivate}
+  final bool closeOnActivate;
+
   /// The widget displayed in the center of this button.
   ///
   /// Typically this is the button's label, using a [Text] widget.
@@ -1292,6 +1307,7 @@ class CheckboxMenuButton extends StatelessWidget {
       ),
       clipBehavior: clipBehavior,
       trailingIcon: trailingIcon,
+      closeOnActivate: closeOnActivate,
       child: child,
     );
   }
@@ -1332,6 +1348,7 @@ class RadioMenuButton<T> extends StatelessWidget {
     this.statesController,
     this.clipBehavior = Clip.none,
     this.trailingIcon,
+    this.closeOnActivate = true,
     required this.child,
   });
 
@@ -1436,6 +1453,9 @@ class RadioMenuButton<T> extends StatelessWidget {
   /// An optional icon to display after the [child] label.
   final Widget? trailingIcon;
 
+  /// {@macro flutter.material.menu_anchor.closeOnActivate}
+  final bool closeOnActivate;
+
   /// The widget displayed in the center of this button.
   ///
   /// Typically this is the button's label, using a [Text] widget.
@@ -1483,6 +1503,7 @@ class RadioMenuButton<T> extends StatelessWidget {
       ),
       clipBehavior: clipBehavior,
       trailingIcon: trailingIcon,
+      closeOnActivate: closeOnActivate,
       child: child,
     );
   }

packages/flutter/test/material/menu_anchor_test.dart

@@ -2799,6 +2799,82 @@ void main() {
       expect(radioValue, 1);
     });
   });
+
+  testWidgets('MenuItemButton respects closeOnActivate property', (WidgetTester tester) async {
+    final MenuController controller = MenuController();
+    await tester.pumpWidget(
+      MaterialApp(
+        home: Material(
+          child: Center(
+            child: MenuAnchor(
+              controller: controller,
+              menuChildren: <Widget> [
+                MenuItemButton(
+                  onPressed: () {},
+                  child: const Text('Button 1'),
+                ),
+              ],
+              builder: (BuildContext context, MenuController controller, Widget? child) {
+                return FilledButton(
+                  onPressed: () {
+                    controller.open();
+                  },
+                  child: const Text('Tap me'),
+                );
+              },
+            ),
+          ),
+        ),
+      )
+    );
+
+    await tester.tap(find.text('Tap me'));
+    await tester.pump();
+    expect(find.byType(MenuItemButton), findsNWidgets(1));
+
+    // Taps the MenuItemButton which should close the menu
+    await tester.tap(find.text('Button 1'));
+    await tester.pump();
+    expect(find.byType(MenuItemButton), findsNWidgets(0));
+
+    await tester.pumpAndSettle();
+
+    await tester.pumpWidget(
+        MaterialApp(
+          home: Material(
+            child: Center(
+              child: MenuAnchor(
+                controller: controller,
+                menuChildren: <Widget> [
+                  MenuItemButton(
+                    closeOnActivate: false,
+                    onPressed: () {},
+                    child: const Text('Button 1'),
+                  ),
+                ],
+                builder: (BuildContext context, MenuController controller, Widget? child) {
+                  return FilledButton(
+                    onPressed: () {
+                      controller.open();
+                    },
+                    child: const Text('Tap me'),
+                  );
+                },
+              ),
+            ),
+          ),
+        )
+    );
+
+    await tester.tap(find.text('Tap me'));
+    await tester.pump();
+    expect(find.byType(MenuItemButton), findsNWidgets(1));
+
+    // Taps the MenuItemButton which shouldn't close the menu
+    await tester.tap(find.text('Button 1'));
+    await tester.pump();
+    expect(find.byType(MenuItemButton), findsNWidgets(1));
+  });
 }
 
 List<Widget> createTestMenus({