Most macs with screens less than 27 inches get a maximum of 12 Genius Mix playlists if you have genius turned on in the view.
There are clearly more than 50 genres on the iTunes store and I've easily seen more than 20 mixes on various people's libraries. I'm not sure if Apple has disclosed how this is curated or how many categories are possible at any point in time.
You can remove a certain list to make room for another Mix by right-clicking on an existing mix icon. As you add more music and the genius updates, you may get a new mix when it can identify enough music in one of the mix categories.