The Oxford Pocket Dictionary and Thesaurus-American Edition states:
Marriage: legal union of a man and a woman.
Then there is:
→ Monogamy: practice or state of being married to one person at a time.
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→ Bigamy: crime of marrying when one is lawfully married to another person.
→ Polygamy: practice of having more than one spouse at a time.
Now is the new word in the vocabulary: gaylesbitransogamy?
Or how about synthogamy? syn is the prefix meaning ‘connoting’, ‘with’, ‘together’, ‘at the same time.’
Alberta Schroeder, Boise