Be sure to try out Turanga:
http://www.warlordgames.co.uk/?p=9287
Live online bughouse would be great fun. Failing that, live online Extinction would be great (IYT has it in turn-based form).
I like reversi too, I think chess.com should add that as well. It's a lot like chess but it's different and fun to play.
And I played 3 way chess one time, I though it was fun because you might get attacked by two players at once so you had to be careful if you made one guy mad you might get ganged up on!
Just a suggestion :
No queens (2 kings represented by queens), pawn can't attack on it's first move.or check out Cirondo, it's a round chess board and it has the possibility of a 4-player game. It starts with only pawns and bishops (16 of them both with 2 players, and 8 of them both with 4 players). Pawns automatically promote to queens if they reach the middle).
I like reversi too, I think chess.com should add that as well. It's a lot like chess but it's different and fun to play.
I think chess.com is pretty focused on chess and only chess. Someday they might add chess960 and possibly other variants.
If you want to play reversi, you should check out playok.com. They have many interesting games, including some historically significant games and chess variants. (9 men's morris, shogi, reversi, others.)
If you like even more obscure abstract strategy games, boardspace.net and iggamecenter.com are extremely good sites. However, there aren't many players who go there at any given time, so you might not find an opponent for the game you want to play.
I have a 4 player chess board myself and I also enjoy playing it with 2 to 4 players. Online play would be nice for practicing.
And this interesting history on 4 Handed Chess
http://www.chessvariants.org/multiplayer.dir/4players.html
You can also play this variant at echochess.com
I think Chess.com should make some extra varients such as 4 way chess. I love playing 4 player chess with my friends but i would like to be able to play it at anytime. Four player chess is really fun and it adds a new twist to the game. So I think that it would be a nice improvement to have Chess.com add some chess varients other than Chess960.