Overwatch implements an Elo system for 6v6 competitive multiplayer. Over the years they've had to make a lot of tweaks to make it kind of work. For example groups are rated by average Elo, but the system doesn't allow you to cause large Elo differences within a team. Also it differentiates between "premade" groups and groups assembled by matchmaking, since the former are assumed to be more coordinated. It also tries to be really smart about how Elo points get distributed within the team on win/loss (which causes a heap of other problems).

Overall you can make it somewhat work, but Elo really isn't well suited for anything larger than 1v1