Only for correspondence actually. You can have more than 2 live games against the same person at the same time. If you already have two correspondence games with a user and you try to accept a challenge from that user, it says “Already playing a correspondence game with this player, consider sending a direct challenge instead”.
See also Correspondence: same player restriction looks great!
Edit: I must correct myself, it applies also to live games. I got confused because once I played 4 live games at the same time with the same person but they were direct challenges.