Pennsylvania has 4 in that list, which gives it more than most nations on the planet: The University of Pennsylvania (19), Carnegie Mellon University (37), Penn State University (in the 50s), and Pitt (in the 60s). I have not parsed it all, but Pittsburgh is in rare company with just a few US cities having more than one named institution.
But here is something to note. Of the 4 Pennsylvania institutions on that list, which ones are taking in folks locally? This is what I get looking that up.