Soooooort of. Space is finite. Sure we have a ton of unused space, but space near harbors, is a premium. New York City cannot expand, not without a massive rail infrastructure.
Anything that "brings in more space" in any shape or form requires a really solid investment in rail. But unfortunately this is not something the US can do effectively.
New York City, even Manhattan, is not terribly dense compared to other major world cities. You can see in this map[0] that vast swathes of Manhattan are occupied by buildings 10 stories or less.
How dense do we want it to be? Density becomes misery after a certain point. Manhattan isn't dense enough, we're showing, but do you enjoy taking a crowded train during rush hour? Have you ever been to a supermarket where the entire inside is one long line of people pulling items into their baskets as they go, ending up in another line where numbers are called to registers.
How about a big apartment building with 10 apartments on the floor, with at least one neighbor per weekend having a party, and half the people letting their doors slam whenever they come and go at night or early morning?
Folks, good news for you - one unit will be available soon, I'm happy to add a vacancy to this delightful city as I age out of it.
Density is not one size fits all. A walkable city guy my whole life, my mental health has taken a real beating. Density is for the young, that's the bottom line. Anyone who is a light sleeper or doesn't enjoy going out a lot at night is just taking one for the team.
Paris is the best example of how you can get very high density without actually needing very large buildings, just by being extremely consistent about having apartments and condos be the default mode of urban construction.
Look at the neighborhoods outside of Manhattan and you'll see plenty of places already near transit stations that could easily double or triple capacity just by putting in townhouses or triplexes.
Anything that "brings in more space" in any shape or form requires a really solid investment in rail. But unfortunately this is not something the US can do effectively.