I thought it was illegal in the U.S. to have more than one spouse.
I think it only applies to lawful wife. I'm not aware of anywhere in the world where it is an issue to have more than one common law wife and family. I think in western parlance, it’s just referred to as the "other women."
But I kinda feel it is also bizarre that so many people launch into "micro-mirages." AKA as serial relationships; for a few weeks, months or years. But in such periods they behave the same as it married. Ie, expecting fidelity and accord in how each other behave. Would seem to be a recipe for disappointment.