Qualia Soup recently posted another good video.
I should definitely bring this up next time I come across a dualist trying to argue that something's "non-physical." I'm essentially a neutral monist who just calls that one type of stuff "physical" or "material." If we were to discover something that would now be called "supernatural," it wouldn't uproot too much of my general worldview: About all that could be said is that such things are made of some particularly exotic type of material/physical stuff. It'd be about like the confirmation of dark matter: Some weird stuff with limited interaction with what we're familiar with (baryonic matter).
I don't see any reason these sorts of things would be beyond science in principle. The only pragmatic barriers I can imagine are the sorts of things believers would not readily grant: Extreme rarity, inherent randomness (utter unpredictability), or ridiculously bad luck that prevented scientifically minded people from preparing tests.
I'm not pessimistic enough to think we can be defeated so completely by alleged weird stuff.