New online-only idea: Backtracking!
No more not daring to look at your hand before it's your turn in a Possession game, because you don't know if you'll play a normal or possessed turn with that hand. With BT-Possession your hand, deck, and other cards are restored to the same configuration afterwards, so you will get to play this hand. In fact, while being Possessed you will gain some handy information, like what's on the top of your deck.
(But what if you for example Masquerade a card during your BT-Possessed turn? No worry, the backtracker will magically find an extra copy for you. And the card that (possessed) you got during that turn is totally gone. BT-Possession doesn't need to say anything special about your cards being trashed, because you get them back as part of the normal backtracking.)
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BT-Possession only restores the situation for one player (which is why it can change the total number of cards). There's also the possibility to go back in time for everyone: There's the Let's Try That Again! Event that you can buy for $7 when everything seems lost. "Restore the total game state to what it was after the first N turns, except that N is one higher. At the beginning of the game N=0. You can't buy this until after turn N".
So the first time it's like a total replay, but then more and more of the game gets fixed, until defeat is unavoidable.