The drag & drop of menus applies also between different menus. Click menu buttons and simply drag your button from one menu to a place in the other menu.
On Exai's site builder one of the unique features is that the drag & drop system works not only within a menu itself, but also between menus. This means you can take a category from one menu and transfer it to the other with the simple drag & drop system. This makes editing menu buttons and categories much easier.