Would it work legally? Sure if it got passed as an amendment to the constitution. As currently structured there basically is zero legal argument with that other than another constitutional amendment.
The chance of that happening with the actual political situation in the USA is essentially zero. To be clear it isn’t actually zero but I. The same way that your chance of walking out the door and dying by direct meteor strike isn’t zero but it isn’t worth planning for over a large number of far more likely things to happen.
If that amendment both directly allowed shared ownership of property for things like high rise apartments/condos and for companies to function as management but not owners I do really think it could work. I’m sure companies could abuse that management position of course but still a huge improvement over our current situation.
As a self response I should add that since you asked about legality I’m this what it would take with the existing government structure. I think the chance of there being a full on revolution and government rebuild from the ground up is more likely than the idea above.