Usually only one or two of any CMx2 game. Can't promise a good turn rate if work picks up so keep it low to be safe, also not fair on opponents. Also I'm that odd CM player that doesn't mind the AI.
I usually have 5 games going at one time. Five (5) is my limit. If I get a request to play, I have to turn them down until one of my five game is done then I contact them to see if they are still interested and available.