The onerous 1967 UN Treaty on Outer Space precludes commercial development of that nature. You can take your own gear there and bring it back. You can collect data. You can build a lunar hotel for tourists out of your own materials. You might be able to collect moon rocks for analysis. But you can't use celestial materials to build things, not asteroid mining, not Martian water, nothing like that.
Noone has really achieved a satisfactory answer to that question yet. The Outer Space Treaty, of which we are a signator (sp?), seems to imply that governments can't claim property in space while individuals and private companies can. I believe this is the only current guidepost that we're going by. I think that once we develop real economic interests on the moon and other places that this treaty can be tossed aside as easily as the ABM treaty. Though this treaty isn't really a hinderance to business in space as it now stands.
It's mine.
One of my very distant ancestors called it.
Check with D. D. Harriman (The Man Who Sold the Moon, R. A. Hainlein, somtime in the 50's).
From a practical standpoint, I don't think anyone would do a thing to stop them. There may be legal challenges from the UN possibly, but who the h#ll are they? The US, if we have the right president when this occurs,could simply bow out of the Outer Space Treaty and then claim the moon for ourselves or the ground surrounding any bases we have there. Then the question becomes who's going to stop us? I don't think we'll have any serious challengers.