The closest thing we have is the amendment process. In theory we could use that to rewrite the entirety of the constitution[0], but good luck getting the required votes in place on any possible replacement. The bar is pretty high: amendments need to be proposed by either a vote of 2/3 of Congress, or by a constitutional convention convened by 2/3 of the state legislatures, and then ratified by 3/4 of all state legislatures.
We couldn't get that sort of agreement to pass something as theoretically uncontroversial as the Equal Rights Amendment. It's laughable to think we could pass a "new constitution" that way.
I expect the only way we could end up with a new constitution is through a bloody civil war, or some sort of coup. Hopefully no one wants something like that, though. I certainly don't.
[0] Technically the entirety of the constitution can't be amended; Article V, Section 5 prohibits an amendment from changing each state's equal representation in the Senate. Though I suppose a "rewrite amendment" might get around that by preserving the Senate as-is as a ceremonial body without any power. That would certainly violate the spirit of that wording in Article V, so I imagine it would be challenged in court.