He admits that if same-sex marriage is allowed, there doesn't appear to be any reason to reject polygamy or other relationships
Boston College law professor Kent Greenfield, a supporter of same-sex marriage, wrote a piece in The American Prospect considering whether fears that legal recognition of same-sex marriage could lead to legalized polygamous marriages, and even incestuous marriages, were accurate all along.
You know those opponents of marriage equality who said government approval of same-sex marriage might erode bans on polygamous and incestuous marriages? They’re right. As a matter of constitutional rationale, there is indeed a slippery slope between recognizing same-sex marriages and allowing marriages among more than two people and between consenting adults who are related. If we don’t want to go there, we need to come up with distinctions that we have not yet articulated well.
Greenfield then attempts to raise a number of differences between same-sex marriage and polyamory and/or incest, but finds each of the arguments wanting. He concludes: