CustomPress multisite-user defined permalinks?

Hello, when creating a multisite, I notice it’s possible to allow each site admin to define their own permalink structure. I wanted to know if this was somehow possible with Custom Press for custom post types.

The reason I ask, is because we are creating a Custom Post type ‘Product’, but for a restaurant, they would prefer the permalink say ‘Menu item’. Any help would be greatly appreciated. Thanks in advance.