polyamory

polyamoria, monisuhteisuus Any of various practices involving romantic or sexual relationships with multiple partners with the knowledge and consent of all involved.
1992, Deborah M. Anapol, Love without limits, page 4

Some of these are poly intimacy, polyamory, polygamy, omnigamy, multimate, multiple adult relationship, combo, cellular family, expanded family, nonexclusive relationship, intimate friendship and inclusive relationship.