menage a trois vs menage

menage a trois and menage both are nouns.

Word	Noun	Adjective	Verb	Adverb
menage a trois	Yes	No	No	No
menage	Yes	No	No	No

As nouns, menage is a hypernym of menage a trois; that is, menage is a word with a broader meaning than menage a trois:

menage a trois: household for three; an arrangement where a married couple and a lover of one of them live together while sharing sexual relations
menage: a social unit living together

Other hypernyms of menage a trois include family, home, house, household.

menage a trois (noun)	menage (noun)
household for three; an arrangement where a married couple and a lover of one of them live together while sharing sexual relations	a social unit living together