When someone is married to several people at the same time s/he is engaging in polygamy and is identified as a polygamist.

Polygamy is a form of bigamy (bi- being the prefix for two), however, the word polygamy is primarily used when someone is married to many – i.e. more than two (2) – people at the same time.

A bigamist is a polygamist, however, a polygamist may or may not be a bigamist.

Merriam-Webster Online Dictionary
polygamy (noun)
marriage in which a spouse of either sex may have more than one mate at the same time - compare polyandry polygyny
the state of being - polygamous
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