I don't think the 4-player was ever introduced to multiplayer, it was strictly sp at the time.
I'm guessing that for regular matches where it's 1v1v1v1, the player who won overall through all players with the most points would win. In cases with dq, I think it would be a last man standing type situation. That would work for most servers, the player who wins gets to play again, while everyone else gets bumped down and 3 new players fight. Would make queues go a lot faster.
In terms of knockout mode, it would probably be the same as it is now. The players who lost would be fspecd, the player who wins would get moved to the bottom of the queue, four new players fight. This would probably bring problems in terms if there weren't enough players to play the final match, but I guess a 1v1/1v1v1 would still work if players were missing.
Hotseat, be the same as it is now. One player always stays on regardless of win or loss. Three players continuously get swapped around.
Although that's just what I think would work best and move things along quickly. Obviously you could have it so only 1 player loses per match, but that would be tedious and slow and I doubt it could ever work like that.