That presumably quickly gets into a game-theoretic double-triple-etc-bluff affair where you have to assume the host is using his knowledge against you.

If you choose the door with the car, the host will open another door to tempt you, so then you don't switch, unlike in traditional Monty Hall. And if he didn't open a door, well, that means you choose a goat, so you should switch for a 50% chance. Except the host knows you're thinking this. And you know he knows. And he knows you know he knows. And...

Perhaps, iterated infinitely, this eventually resolves into a limiting expected value for switching and not, but I have no idea how to compute such a scenario.