Rotation

From SmashWiki, the Super Smash Bros. wiki

Rotation is a mode of play in Super Smash Bros. Brawl that lets those at home with more than four players swap out and take turns brawling. This mode works with 5-16 players, so if more than 16 would like to play, a tourney must be set up.

Such a mode existed in Melee, but it was a part of it's Tournament Mode as Winner Out/Loser Out Tournaments.