Do you think that's because Manhattan is such a great place to live or because people globally would love a life that's not a life of poverty?

Build more Manhattans.

1. That wasn't the original claim, which was "There should be enough housing for everyone that wants to live in a given area". People don't want to live in Manhattan 2, they want to live in Manhattan.

2. "Build more Manhattans" is easier said than done. Even petro-states with astronomical amount of money to splash around have a hard time building a "Manhattan". Dubai might be very shiny and the financial capital of the middle east, but it's no Manhattan.

Also, "claim" is too strong. This is the __aspirational__ sort of should. "We SHOULD all be kind to each other."

Is that a hypothetical or your actual belief?

I don't know Manhattan very well, only what I've seen on TV and in Movies.

Back of napkin answer:

Build bigger buildings, lots of them. All of those 'quaint' places with 2-6 story buildings? 50-60+ story sky-scrapers.

However that's probably also the answer you assumed. Yes that would change the 'character' of a place, because the only way of keeping that the same is to keep the number and type of people in a place the same. How could someone preserve an idea that directly contradicts a reality? No, there would need to be a new idea that supports the desired conditions. Hopefully a good idea that is well executed.

As another commenter said, 'more ''Manhattans''' is another way, try to replicate the sort of feel / idea at existing scale or larger in other locations.

My own comment was about the technical and physical goals a society should strive for, which are within reach, should we the people have the will to reach for them.