Answer:
A bigamist is a man with two wives.
However, under US state laws involving marriage, only the first marriage would be recognized as legal (until dissolved), and any subsequent ones as a deliberate criminal offense.
In practice, a bigamist is the term for any man who marries again, however many times, while still legally married. Technically, the term for more than two wives would be polygamy. De facto polygamy is practiced by some individuals and in some US religious groups in contravention of existing laws.
Unites States Law:
Bigamy is the crime of knowingly entering into a marriage with one person while still married to another person: someone with two or more wives or two or more husbands at the same time. A person who commits bigamy is a bigamist.