Make it so the owner of a private server has more control over their server, such as the ability to force games to start in whatever game mode they want and create custom game modes.
By custom game modes, I mean allowing private server owners to adjust the spawn probabilities of each role and choose how many of each role spawn in a game. This would allow players to have matches with multiple Detectives, Murderers, or any other roles they want.
Additionally, as you can probably infer, private server owners should be able to override the restrictions that normally prevent certain roles from spawning together.