Can a person have multiple spouses?

No, bigamy (or polygamy) is criminalized in every state in the union. Even individuals who have a sincere religious belief in polygamy cannot legally engage in such a practice. The U.S. Supreme Court rejected a First Amendment based religious freedom defense to a bigamy charge in Reynolds v. United States (1878). The Court reasoned that if it granted George Reynolds a religious based exemption from polygamy, it would make him a law unto himself.