Splatoon 3 tried this already and settled on 2v4v2 for its three-team mode (Tricolor Turf War), because according to a developer interview, they tried 4v4v4 in internal testing and it almost always resulted in one team getting ganged up on all game.
Find some way to remedy that and you've got a good event mode on your hands.
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Thats kinda the idea for tricolor tho It’s supposed to give the other two teams a chance
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Are you locked into one class per account in that game ? Or like D2 have all 3 per account and can switch at will ? Think if want true class wars type game would need to lock you to one class type per account