Oh, sorry I didn't see your post soon enough! My roommate and I were trading Katie back and forth for a little while, but then at some point she must've realized we weren't going to take her anywhere new and left.

llonka, there's not really a lot you do with your own avatar, they don't get their own house or anything so you could possibly share the game. You can change your accessories as much as you like, and once you purchase the styling machine with play coins you can even change your hair and facial features (but not gender or name). So if that doesn't really bother you or your son it's totally feasible to just trade off designing houses.