I think the answer will be to some extent a matter of opinion. I'd say it is material form that requires an explanation in terms of something beyond material form. I suppose we can say that matter arises from matter but not many people think this idea makes sense. I certainly don't.
Then there is consciousness, the background dependence problem, the extra dimensions of string theory, nonlocality and so forth. Then there are all the ancient problems of philosophy, which are undecidable in the absence of something which transcends form. For 'form' here we could read 'extension,' so for physicists who conclude that extension is an illusion of some sort, of which there are many, the universe as a whole would require such an explanation. Or so it seems to me.
At this time there is no fundamental theory of anything which is not predicated on a phenomenon beyond material form, and this suggests to me that no such theory is possible.