I know this from last year because my team did it:
You can play any of the mini factions in place of a main faction. You may only play one copy of each mini faction ID. So Apex, Adam, Sunny, Prof is a valid set of IDs for the team.
I think also, and @spags will have to confirm this, if you play a mini you can still duplicate a main faction. If this is indeed the case, Adam, Sunny, Val, MaxX would be a valid team.