This paper argues that the four most plausible arguments compatible with public reason for an outright legal ban on all forms of polygamy are unvictorious. I consider the types of arguments political liberals would have to insist on, and precisely how strongly, in order for a general prohibition against polygamy to be justified, while also considering what general attitude towards "marriage" and legal recognition of the right to marry are most consistent with political liberalism. I argue that a liberal state should get out of the "marriage business" by leveling down to a universal status of "civil union" neutral as to the gender and affective purpose of domestic partnerships. I then refute what I regard as the four most plausible rational objections to offering this civil union status to multi-member domestic partnerships. The most common objection to polygamy is on grounds of gender equality, more specifically, female equality. But advancing this argument forcefully often involves neglecting the tendency of political liberalism (by whatever name it goes in contemporary, complex, multicultural societies) to tolerate a certain amount of inequality in private, within the bounds of robust and meaningful freedoms of choice and exit. Properly understood, polygamy involves no inherent statement about the essential inferiority of women, and certainly not more than many other existing practices and institutions (including many expressions of the main monotheistic religions) which political liberals regard as tolerable, even reasonable. Arguments from the welfare of children, fairness in the spousal market, and the abuse of family subsidies are also considered and found insufficient for excluding polygamy.