I like your idea. Indeed, sometimes teams are perfectly balanced and you just want to play more lobbies with the same teams. We just need to figure out best way to implement it.
Maybe add a feature that allows to set a "chain" lobby, ergo being able to set amount of matches that should / will be played.
Or add a vote system "Lave lobby open? / Play anothermatch?"
Probably just a new lobby created with players automatically set into the slots they were previously. Ideally there would be a checkbox for the operator to check in case they only want to run one more on their server.
I know the additional work load might not be worth it, but an optional server plugin providing something like !extend functionality would be perfect here. maybe even start a vote to extend the lobby.
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Allow a lobby to stay open after a game has ended