What's the noun for polyandries? Here's the word you're looking for.
polyandry
The having of a plurality of husbands at the same time; usually, the marriage of a woman to more than one man, or the practice of having several husbands, at the same time.
(zoological): The mating pattern whereby a female copulates with plural males.
“Then this so sweet maid is a polyandrist, and me, with my poor wife dead to me, but alive by Church's law, though no wits, all gone, even I, who am faithful husband to this now-no-wife, am bigamist.”