Does the USA have any laws that limits how many times you can get married?
Yes, 52+ counting only federal law, state law, and district law,
you can only be legally married to one person at a time
It is illegal in some jurisdictions for parties of more than two to establish a common residence* and present themselves as married. This is treated as if it were bigamy (enforcement is vanishingly rare... and an attempt to get the courts to legislate from the bench failed because the sisterwives family was not actually pending prosecution).
* in common law states presenting your self as married has force, i believe if you actually reside together