What you describe sounds similar to "vote chess." You can play this on chess.com and many clubs have vote chess team matches against other clubs already!
https://support.chess.com/article/441-how-do-i-play-vote-chess
"If Chess.com would only listen to me, It'd be twice as fun and popular!!"
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It's indeed similar, but there are differences. I just now tried it, and it isn't 'exactly' playable. I'm asking for a regular game in which 2 players are teamed against another 2, in a normal rapid or blitz game. No voting, just each player suggests moves and if your partner seconds a suggestion, it goes.
(Or if it's 3 players, then say 1 guy suggests, then it's shown as blue, if 2 suggest, it turns red, and with 3 it goes.)
I really don't understand why this feature isn't added. It doesn't change the game rules or format in any which way whatsoever, and everyone can still employ all their theory study.
All it does is add a new fun element to chess.
Tried already. You can also.
Adding a real co-op mode to chess would be a great way to expand the game, and make it more fun. The best way to add co-op to regular chess is to make that two (or even 3) people must agree in order for any move to be played. Any move you attempt is shown as a suggestion to your partner. If they second it, it goes. In low time, or whenever chosen, any of you can move, simply whoever goes first.
(A 2nd option is that every second move is traded off between the two, and a 3rd is that one picks the piece, the other moves it.)
Players can choose who to partner with, just as one chooses to play against a friend.
If chess.com would only add this feature, it could literally bring them in millions!