It's either multiamory or or polyphilia. But mixing Greek and Latin roots? Wrong!
Saw that on a t-shirt and it reminded me of this place, and, hey, I'm a language geek, so it tickled my fancy.
(Just in case anyone wants to complain, I have no particular opinion of the practice of having multiple love relationships, and I have friends who live that lifestyle. I don't judge, and I'm not bothered. I just thought the t-shirt was funny.)