One thing I've seen a lot in crossovers with ASOIAF is characters from other worlds being dropped into Westeros with all their knowledge, and then that knowledge being subverted. The twist isn't that they have the info, but that it's actively wrong or dangerous. A Hermione Granger fic had her using magical forensics to "prove" Tyrion didn't kill Joffrey, only to have Littlefinger frame someone else entirely because he'd already anticipated a truth-seeker. Her meta-knowledge made her a predictable piece, not a game-changer.
Another popular one flips the 'Stark Wank' trope. A crossover brings in a powerful force to back the Starks, making them seem unstoppable. The twist is that this external power fundamentally changes the family, corrupting their honor or making them arrogant, leading to a new, arguably worse, form of tyranny. I read one with the Jedi Order arriving to advise them, and by the end, Robb was basically a Sith Lord justifying conquest with a lightsaber. It's less about good guys winning and more about power distorting even good intentions.
My personal favorite is when the crossover element itself is the twist. The story seems like a standard political drama in King's Landing for 20 chapters, and then a White Walker scout reports seeing a giant robot on the horizon, or a character has a sudden, horrifying realization that the 'red star' in Melisandre's prophecies isn't a comet—it's the Death Star.