I used to hate Possession. But I've learned to love it. It can make the entire dynamic of the game wonky, and I like that. Some random thoughts on it:
(1) Possession is a fancy Workshop-variant (can't remember where I first heard that; I definitely didn't make it up).
(2) I used to avoid at all costs getting Masquerade, Ambassador, or Island when there is Possession, especially if there are ways to play multiple Possessions per turn. But I actually think there are many cases where it's a good idea to get them.
- Ambassador -- if you get an Ambassador and your opponent doesn't, and there is no real immediate defense against it, you can just get such a large early lead and slow your opponent down so much, potentially to the point where they're never going to be able to afford a Possession.
- You can always buy 2 Ambassadors, with plans of eventually passing one to them, in which case you're both in the same boat. Same goes for Masq.
- If there are ways to trash your early Amb/Masq, then you might as well still get them
(3) Never ever ever resign on a Possession game. They can get so wonky, you never know when you can pull off that crazy 3-pile.
(4) There are interesting "defenses" against Possession -- cards that make your opponent discard, cards that give you VP chips, Golem (which your opponent won't want to play and reveal a Possession), etc.
(5) Don't play Durations (especially Tactician), get a big Native Village mat, or accumulate a bunch of coin tokens if your opponent may play Possession
(6) Don't even try to understand the Possession-Outpost "synergy"
(7) If your opponent has a good deck, then the best defense against your opponent Possessing you isn't greening or building a bad deck; it's Possessing them more.
(8 ) It's fun upgrading Cities on your turn, then reaping the benefits on your opponent's [possessed] turn.
That's all I can think of for now. There's probably a ton of other stuff.