Base Coup is best at around three players. Past that it gets diluted: with a big table, the risk-reward of calling someone out collapses. Most of the time, do you really want to be the one to stick your neck out and challenge?
You can team up with others to challenge by randomizing. E.g. with 4 players, the other three can agree to randomize who should challenge, with a 1⁄3 chance each (or any other distribution; you can negotiate over this). The player who’s then chosen by the randomization could still not go through; the rules don’t oblige them to. But it’s anti-cooperative and other players won’t appreciate it and can punish you later.
You can team up with others to challenge by randomizing. E.g. with 4 players, the other three can agree to randomize who should challenge, with a 1⁄3 chance each (or any other distribution; you can negotiate over this). The player who’s then chosen by the randomization could still not go through; the rules don’t oblige them to. But it’s anti-cooperative and other players won’t appreciate it and can punish you later.