It’s hard to say how many people in the United States practice polygamy — estimates vary widely, from 20,000 to half a million — but it’s clear most of their fellow Americans disapprove. In a 2013 Gallup poll about morally controversial issues, a mere 14 percent of the public said they accepted polygamy (only adultery and cloning humans had lower approval rates). An earlier poll found two-thirds of the public felt the government had a right to outlaw the practice, which typically takes the form of a married man also living in a marriage-type relationship with other women. So don’t read too much into the popularity of TV shows like “Sister Wives” and “Big Love.” The country is not ready for plural marriage.

Certainly that was a bet Chief Justice John G. Roberts Jr. was willing to make last year. In his dissent in Obergefell v. Hodges, the Supreme Court case that recognized a right to same-sex marriage, he sought to capitalize on widespread discomfort with polygamy: “It is striking how much of the majority’s reasoning would apply with equal force to the claim of a fundamental right to plural marriage.” The majority had outlined a right to marriage that could not be constrained by historical definitions or legislative whim. But if there was nothing special, legally speaking, about the man-­woman aspect of traditional marriage, what was so special about the two-person aspect?

Roberts intended his argument as a reductio ad absurdum, assuming that defenders of same-sex marriage would be alarmed by the implication. While some rose to the bait — the same-sex marriage advocate Jonathan Rauch, for example, was quick to offer arguments for why polygamy was different — other progressive thinkers, like the political philosopher Elizabeth Brake, embraced the opportunity to explore novel possibilities for marriage reform. In the essay collection AFTER MARRIAGE: Rethinking Marital Relationships (Oxford University, paper, $29.95), edited by Brake, she and nine other philosophers consider what further consequences might be implied by the principles of the same-sex-marriage movement — ­including, notably, the “disestablishment of marriage itself.”

As traditionally understood, a liberal state lets individuals decide for themselves, whenever possible, how to live, and so it can’t justify its policies solely by appeal to controversial moral doctrines. Yet only such doctrines, progressives have argued, could justify limiting the benefits of marriage to male-female couples (or, in an earlier era, to single-race couples). Extending this logic, Brake suggests that the same principle forbids the state to limit the benefits of marriage to romantic-love dyads — which represent just another “controversial conception of the good.” Surely, she speculates, there are other legal arrangements, less exclusive and less burdened by their history than the institution of monogamous marriage, which could offer support to adult partners, children and caregivers. Contributors to her volume entertain some possibilities: relegating marriage to private contract; replacing marriage with a parenting agreement; modeling marriage on friendship instead of romantic unions; recognizing temporary marriages (those intended to last for only a set time); and allowing polygamy.

Not all the essays are so strenuously avant-garde. One of the more nuanced pieces, by the philosopher Peter de Marneffe, articulates a liberal position on polygamy that opposes its legalization but also its criminalization. The government, according to this view, may legitimately withhold the benefits of marriage from adults in polygamous relationships (on grounds that such relationships characteristically deprive children of material and emotional resources from their father), but may not prosecute them, as is currently possible in some states, for polygamous cohabitation (because this is private consensual sexual activity). Here, de Marneffe finds himself in agreement with the law professor Deborah L. Rhode. In ADULTERY: Infidelity and the Law (Harvard University, $28.95), Rhode concludes that “perhaps the most plausible solution” to the problem of polygamy is partial legalization: invalidating criminal laws against cohabitation but retaining the prohibition on multiple marriage licenses.

In the United States, polygamy is technically a form of adultery, since it involves sexual relations between a married person and someone who is not his or her legal spouse. Adultery remains illegal in 21 states. Rhode, though no fan of adultery, argues that it should not be prohibited by law, because such laws infringe on our constitutionally protected right to privacy — and have proved woefully ineffective, in any event, at protecting the institution of marriage. Laws criminalizing polygamous cohabitation have comparable flaws, she observes.

Rhode is sympathetic to efforts to get the government out of people’s bedrooms, and she even notes that polygamy sometimes offers benefits, and not just to the men involved: “Some Mormon women consider polygamy a solution to such difficulties as single motherhood, poverty, loneliness and work/family conflicts.” And among some African-American women, she reports, an arrangement known as “man sharing” is considered a route to family stability in communities where high rates of imprisonment and unemployment have created a shortage of potential husbands. But Rhode also cites evidence of practical problems with formally legalizing polygamy. After World War II, France, looking to increase its labor supply, allowed the immigration of polygamous families from Africa — only to encounter difficulties with coerced marriages and excessive demand for government benefits.