I had a rough idea for a variant based upon the concept of Rengo.
Basically, the game begins like a typical Rengo game. Let’s say 3 players on each team, for this example. However, at some predetermined point in the game, such as 50 moves in, (if the game has not already ended by resignation or time out) the game forks into 3 separate games, each continuing from that point, with just pairs of players playing out each game.
Essentially, this would be like playing Rengo during the opening, to jointly create a common fuseki, but then playing that position out multiple times across the different pairings through the middle and end game. The pairs could either be drawn randomly or by strength from the original teams. The final outcome of the entire match would be decided by the total number of forks won by each side.
Of course, while playing out the forked game, none of players should observe what is happening in any of the the other games, so that each fork evolves independently.