User specific permission to add links to a menu

When I create a content type, e.g. ‘Basic Page’ and I want to add a link to a menu I do usually the following:
Menu settings -> Provide a menu link -> choose a menu and its position of the link there

I know, that I can define, which menus are appearing here, in the menu settings section of a content type.

I have several menus, for specific users. For now, if they create a new ‘Basic Page’ they see all the menus, which are set for this content type. So as well, menus from other users. Is it possible to show just their own menu, so they do not have access to the other menus?

For now I solve this problem by assigning roles for each individual user, and granting permissions for this ‘user role’ per ‘user menu’, by using the Menu Admin per Menu module for D7. It would be much more convenient, to use user specific permissions here.

Is there any way, of doing that?

Thank you in advance!