Legalizing Polygyny: What Would It Take?

Families that follow the Islamic religion, the Mormon religion, and certain other religious sects that practice polygyny (a man marrying multiple wives) could conceivably make the case that they have a right to legally do so under the First Amendment guarantee of Freedom of Religion. But the historic battle between the Protestant and Mormon faiths in the early days of American history lead to the banning of this practice, as the Protestants sought dominance over the Mormons and the Mormons allowed polygyny and the Protestants did not. However, what has emerged today is a new set of imigrants and converts to Islam, a religion of which allows polygyny for the purpose of providing support for orphaned children and widowed women.  America has allowed same sex marriage. Religious communities have asked, when will America consider the rights of heterosexual women, who greatly outnumber available heterosexual men? Don't they have a right to a legal marriage, if all the consenting adults agree to an arrangement in which a married man may legally marry an additional wife?  Would an elected official be willing to put forth legislation to the effect? Would a federal lawsuit need to be filed? Are women who are tired of being single be willing to take the lead in this effort?