For decades, opponents of marriage for same-sex couples have appealed to polygamy. The Chief Justice’s dissent in Obergefell is no exception insofar as he says that the logic of the majority opinion with respect to same-sex marriage also applies to plural marriage. This paper explores the resources for distinguishing polygamy from same-sex marriage, focusing on the mutability or immutability of the desire to engage in plural/group marriage as compared to the desires to marry someone of the same sex. It shows the appeal to immutability does not succeed in distinguishing plural/group marriages from same-sex marriages.