Nothingness: Very similar to loop chess, but your partner gets the pieces you capture. It would be fairly easy to implement (I think). Each game could go on independant of each other. You would need to be able to see your partner's game.

Nothingness: You're thinking of Bughouse. I'd like to see it here as well, but it may not be so easy to implement.

Also, I'd like to echo a recent request for Crazyhouse, which in my opinion is a better game than Loop Chess.

KotDB: I love Bughouse, believe me, but I don't support it to be implemented here. Bughouse requires to be live and fast-paced to be of any fun. To play it turn-based you would probably have to set up an order of play like (boards are A,B) A white - B white - A black - B black - A white ... It has been done but I don't think that it has been fun :-)
As for Crazyhouse, I fail to see why it should be better than Loop Chess (generally named Chessgi). The only difference is that in Crazyhouse a promoted piece return to pawn after it is captured. The reason of this special promotion rule is obviously to copy over-the-board Bughouse, where you don't have time to seek for a promoted piece and you continue to play with one or more pawns which have the power of a queen ; it is already hard to remember that they were promoted while they stay over the board but it would be impossible to remember it once they are taken, so the only way to handle promoted pieces is to state that they return to normal pawns once captured.
So the only advantage of Crazyhouse over Loop Chess is that Bughouse players are more acquainted to it. This being said, it is less logical, and a completely correct user interface for it would require to place markers on all promoted pieces, as they behave differently from normal pieces once they are captured.
Rather than Crazyhouse, there are two other excellent games in the same family, namely Recycle Chess and Hostage Chess. Recycle is not hard to implement, Hostage is harder.

nabla: Recycle Chess with or without pawn promotions?

Fencer: Yes, good question, the link I gave is slightly outdated. It looks like Recycle Chess is now always played with promotion, and it is also the way I played with the inventor some months ago. Of course it makes a huge difference : pawn drops to the seventh rank are very common when playing with promotions.

nabla: Hostage Chess looks like fun, and it can be played on a regular board (unlike loop et al where the pieces change color).

grenv: Yes, and the same is true about Recycle Chess.