Team tournaments with individual bracket pairings
In Chess, especially in the scholastic USCF tournaments, there is a system for playing Swiss tournaments with teams. Swiss tournaments are widely understood but there is a system they use to make teams work.
Teams are created and can be edited with adding or removing players anytime. Whenever someone registers for a tournament, they register their teamname along with their own name. This allows team statistics to be calculated. On Challonge, the "Team" option is just the same as playing as an individual player with a team name. There is really no way of playing swiss tournaments, for chess or any game, with individual players, each of who contribute to their team scores. I really would like to see this happen on challonge.