Try to make only 1 submenu at a time be opened.

Doesn't work as there is currently no logical tree link between
MenuItems as they're in Popups. Need to fix this first,

Perspex.Controls/IMenu.cs

@@ -9,5 +9,7 @@ namespace Perspex.Controls
     internal interface IMenu
     {
         void ChildPointerEnter(MenuItem item);
+
+        void ChildSubMenuOpened(MenuItem item);
     }
 }

Perspex.Controls/Menu.cs

@@ -37,6 +37,14 @@ namespace Perspex.Controls
             }
         }
 
+        void IMenu.ChildSubMenuOpened(MenuItem item)
+        {
+            foreach (MenuItem i in this.GetLogicalChildren())
+            {
+                i.IsSubMenuOpen = i == item;
+            }
+        }
+
         protected override void OnAttachedToVisualTree(IRenderRoot root)
         {
             base.OnAttachedToVisualTree(root);
@@ -58,7 +66,7 @@ namespace Perspex.Controls
         {
             foreach (var i in this.GetLogicalChildren().Cast<MenuItem>())
             {
-                i.IsSubMenuOpen = false;
+                i.IsSubMenuOpen = false;               
             }
         }
     }

Perspex.Controls/MenuItem.cs

@@ -16,7 +16,7 @@ namespace Perspex.Controls
     using Perspex.Rendering;
     using Perspex.Controls.Templates;
 
-    public class MenuItem : HeaderedItemsControl
+    public class MenuItem : HeaderedItemsControl, IMenu
     {
         public static readonly PerspexProperty<ICommand> CommandProperty =
             Button.CommandProperty.AddOwner<MenuItem>();
@@ -59,6 +59,18 @@ namespace Perspex.Controls
             set { this.SetValue(IsSubMenuOpenProperty, value); }
         }
 
+        void IMenu.ChildPointerEnter(MenuItem item)
+        {
+        }
+
+        void IMenu.ChildSubMenuOpened(MenuItem item)
+        {
+            foreach (var i in this.Items.Cast<object>().OfType<MenuItem>())
+            {
+                i.IsSubMenuOpen = i == item;
+            }
+        }
+
         protected override void OnPointerEnter(PointerEventArgs e)
         {
             base.OnPointerEnter(e);
@@ -84,6 +96,10 @@ namespace Perspex.Controls
                     item.IsSubMenuOpen = false;
                 }
             }
+            else if (open)
+            {
+                this.GetLogicalParent<IMenu>()?.ChildSubMenuOpened(this);
+            }
         }
 
         private static void SubMenuOpenChanged(PerspexPropertyChangedEventArgs e)

TestApplication/Program.cs

@@ -166,6 +166,17 @@ namespace TestApplication
                                         new MenuItem
                                         {
                                             Header = "Save As",
+                                            Items = new[]
+                                            {
+                                                new MenuItem
+                                                {
+                                                    Header = "Sub Item 1",
+                                                },
+                                                new MenuItem
+                                                {
+                                                    Header = "Sub Item 2",
+                                                },
+                                            }
                                         },
                                         new MenuItem
                                         {