Will Ivy League Schools take more than 1 from each school?

"It really seems, to one for whom this conversation makes the selective high schools seem like part of a machine, that except in rare cases, it is the same schools who have students getting into the top colleges. "

Yes. But that also makes sense from a logical standpoint given how the selective high schools operate. In our county, the vast majority (in excess of 90%) of the high achieving students attend the magnet school so there’s a concentration of applicants with high test scores, interesting ECs, etc. If 90%+ of the potential candidates for selective colleges are concentrated in one area school it shouldn’t be surprising that more of the applicants from that area school are selected. There’s just a larger pool of candidates. So yes, in our area highly selective colleges will take more than one student from the magnet school but since most of the qualified applicants are from the magnet, that makes sense.

That being said, I think many of the colleges get lazy and stick to admitting students from HS that the college is familiar with. That tendency definitely gives applicants from known HS an admissions advantage.