Is there any way to set up a match where two players can play against two players without them being in teams or groups. To clarify Player A would play a game against player C and a game against player D. Player B would do the same. So A and B vs C and D.  Thanks

You are speaking about a Scheveningen match, like they play when it's the Veterans vs Women, each player plays all the players on the other team individually, but none of his own team.  No, you can't do that here as far as I know other than by issuing individual challenges for each game.

You can set up a 4-man round robin where all play the other three, but in that case A must play B, too.

Why not have partner chess games, man/ women play man/women partners, one player in each partner team with a higher rating than the other, one game with black one game with white. Not only would the lower partner pick up tips, but on making blunders would create some interesting comments from the higher rated partner,or vice/versa, should be fun.Each individual in turn would make the next move without discussion between partners,(don't think we need to cheat )that's all you have to do is give your password to play the same game to your partner.SCUT to pick the partners. We could have partner championships, some might even get married HA!!