If there are multiple extra turns to be played "after this turn" then you get to choose the order, I believe, unless an Outpost and Possession were played on the same turn, in which case Outpost happens first. I'm pretty sure that's right.
Sure, but this doesn't answer the question asked. The question is...
Turn A: I play Possession-1 and Possession-2.
Extra Turn 1: I make you play Possession-3.
Which happens first, Extra Turn 2 or Extra Turn 3?
I believe:
Turn A: It's your turn. You play Possession twice. This sets up two future effects that try to give the other guy an extra (possessed) turn. At the end of this turn (or between turns), the game decides what the next turn will look like. There are two future effects trying to give the other guy a turn, so he gets to pick which one happens "first." It doesn't really matter which he picks because they're both doing the same thing. (The one that doesn't happen first doesn't get checked again before next turn.)
Extra turn: It's the other guy's turn, but you're driving. You make him play Possession. That sets up a future effect that tries to give you an extra (possessed) turn. At the end of this turn, the game decides what the next turn will look like. There are two future effects; one is trying to give the other guy an extra turn, and one is trying to give you an extra turn. The other guy is the current player, so the turn that happens to him happens "first." (If there were multiple effects trying to give him an extra turn, you'd be controlling him as "he" made the decision of which one happened first.)
Extra turn: It's the other guy's turn again, and you're driving again. You don't make him play any Possessions. At the end of this turn, the game decides what the next turn will look like. There's one future effect trying to give you an extra turn. It happens.
Extra turn: It's your turn, but the other guy's driving. He doesn't make you play any more Possessions. At the end of this turn, the game decides what the next turn will look like. There are no future effects trying to give people extra turns, so the game does back to alternating between players. The last regular turn (Turn A) was yours, so the other guy will be taking his regular turn.
Turn B: The other guy finally gets a normal turn. Luckily, he's drawn three Possessions and two King's Courts.