I do not ask what he would think of 20th century philosophy? That is clear. But the question I ask is more along the lines of what he would do with Kant? [Or the different schools based on Kant--or stemming from Kant?]
I have suggested that he would continue in his approach. That is his way is really a kind of synthesis between Plato and Aristotle. So what I have thought is he would simply continue this process.
Mainly I think he would accept Kant's structure of the mind but he would justify knowledge by a kind of third kind of knowledge that is not reason and not sensed--but known. [The Rambam was not in the habit of denying the truth based on criteria like, "Who said it?' ]
I wish I could show this more clearly but you can see this idea in this essay on Kelley Ross's site.
See also this article in the this Philosophy magazine from Cornell.
If you go with the Rambam (Maimonides) you have to add another kind of knowledge that is known not by sensory perception and not by reason, i.e. immediate non-intuitive knowledge.