So, I don't know if it's a dumb question or not, but I was wondering if is there any rule about doing an MP6 run in Multiplayer. Are there any category that you can do it or it's just against the rules?

All boards runs are 1 player 1 controller only. The only categories on the main board that allow for multiple players are the Individual Mini-Game speedruns and Any%. If you want to do a multiplayer run we could add it to the Mario Party Extension board under a new category. https://www.speedrun.com/mariopartyce