Disclaimer: I haven't tried this yet myself, but it looks like it should work.
Further disclaimer: Don't blame me if a rear-seat passenger is harmed.
The black plastic backs of the front seats have two fairly flat planes, one towards the top that is angled top-forward, and just below that, angled bottom-forward. I believe you could put a
3M Command Strip large clear hook on either surface. I'd use the lower one, so that the jacket hangs straight provided that that is high enough up for your jackets. Holds up to 4 pounds, which should be enough for a jacket and an extra shirt.