Just proposal if this is in any way feasible for team tournaments. Don't think that it is particularly good idea but wanted to see what do you think. Only Single Elimination and Round Robin could have this implemented.

The basics of the tournament will be driven the same way as usual with these exceptions:

Round Robin tournament - number of matches will be reduced to possible combination and max number of matches would be half of the usual number of matches. Each player should play with different team all matches. Each player keeps individual score and at the end of the tournament we could have only one person (not team) winning the tournament.

Single Elimination tournament - for each stage there will be random teams. Proposal is that no 2 players can be in same team during competition, but that is almost impossible, especially for longer tournaments. In this tournament winners are collective, and second place is divided by finalist and all team members that lost against winners in Quarter-finals and further.

IMO, I would like to see how such thing really work, although I don't expect that such tournament would ever be used by players (possible Fizzers's open tournamet?).

Other proposal is to set tournaments so each player applies for team tournament, but teams are fixed after tournament starts. All things in tournaments are as usual.

you could implement them with the CLOT API and test them out.