My original thoughts were that a multi-game deal was some kind of actual deal, for instance; I'll help you win this game, if you play the next one with me and let me win. Or something a long the lines of: I'll give you Outpost A if you give me your inspector in the other game we are currently in. Both of these situations are obviously unfair multi-game deals. But it appears that the general consensus is that any type of agreement made between 2 players counts as a multi-game deal. Most people feel allying with your friend is cheating.
However, my personal opinion is that if people allied with their friends the way they allied with other people it wouldn't be a problem. I'm playing a game with a friend of mine right now, but I'm currently plotting how to destroy him.