I tested whether subsubcategories can already be made in Q2A, and I found out that they already can!
I have made you a moderator for the reviews section so that you could be able to recategorise the papers according to the hirearchial category system (though I still don't know how practical that is), but I don't know if that allows you to add subsubcategories. To check if you can, try accessing this page:
http://www.physicsoverflow.org/trollsouthere14/admin/categories?edit=25