Because this is an unlocked post with possibly contentious content I'm going to be heavy-handed in moderating comments. Be on-topic and be polite or be banned.
I've said before that I thought Obergefell - the case that finally put the stake through the heart of state-level DOMAs - was decided on the wrong grounds. I think the decision is correct - same-sex couples should enjoy equal marriage rights and all states should be compelled to recognize them - but I think the majority opinion erred in finding a "right" to marry in the Constitution.
Instead, I would have preferred to see a decision more solidly grounded in the Constitution and previous caselaw prohibiting sex discrimination. Think about it this way: Alex and Betty wish to marry; this is allowed. Alex and Charles wish to marry; this is not allowed. Confronted with this dichotomy, the Court (rightly, I think) delved into the area of animus. That is, there is a question whether the prohibition on Alex and Charles marrying is based on a hatred or dislike of a class of persons. Although the defenders of DOMA tried mightily to show the opposite, I think the record supports the opinion that prohibitions on same-sex marriage were motivated in large part by discrimination against/hatred of gay people. Laws based on animus are not always unconstitutional but they are immediately suspect, based on the principle that all citizens should be treated equally under the law.
However, if we consider that the Court has not needed to use an animus test in past cases involving sexual discrimination, I think we find ourselves on firmer (legal) footing. Laws that discriminate on the basis of sex are not just suspect but generally understood to be unconstitutional, using the same 14th Amendment grounds that Windsor used, but without the need to reach for a new right. People favoring marriage equality can argue that the prohibition on marriage for Alex-Charles, or Amy-Betty is a discrimination based on the sex of the partner. The government would have to show a really compelling need to justify such discrimination and I expect would have lost.
But that's not what they did. In the most poetic opinion I've ever read from Justice Kennedy, the right of marriage was extolled. And partly due to that, we now get the thorny question of "but what about more than two people." If there's a right to marry one person does that right extend to marrying more than one person? I think it does, sort of, but I want to make an argument that doesn't rely on a decision that troubles me.
Imagine that Alex is married to Betty and Alex also loves Charles. We've established that Alex can now marry Charles, but only if he first divorces Betty. Why is that necessary? When equal marriage was first being discussed someone put together a list of the benefits of marriage that aren't accorded to non-married couples and came up with over a thousand. These include things like inheritance rights (one of the key issues in Windsor), visitation rights, and so on. I want to set these all aside for the moment and just focus on one thing: the ability of polyamorous people to declare themselves married and behave as married.
That is, Alex and Betty and Charles would like to have a ceremony (with, we presume, an approving officiant) that declares their familial status. If they call it an "affirmation" or "committed lifelong relationship" or some other name there is no problem. It's only when they use the word "marriage" that they are prohibited. But that is, prima facie a speech restriction, which I believe is unconstitutional. Why should the government have any say in what word Alex and Charles use to describe their relationship? Why should the government be allowed to prohibit them from behaving as (they believe) married people do? Again, that's a restriction on speech acts which I take to be a First Amendment violation.
If you'll grant me this far, then let me further split the remaining parts of the problem. Two things that some married people do that might be of concern are live together, and act married without other partners' knowledge, including having sex outside of marriage. The first are typically covered under what are called "bawdy house" rules, and are relics that have generally been struck down. These laws have been used against fraternities and brothels and are an indirect attack on behavior that the courts have generally found legal - the freedom of consenting adults to cohabit and to assemble for legal purposes.
The other possibly problematic behaviors are addressed by laws against bigamy (as fraud) and against adultery, which still exist in some states but are rarely enforced. At one time these laws sought to protect women, who were often seen as the victims of philandering men. They also provided convenient cover for couples that wanted to get divorced but then-current laws required some finding of fault. Sleeping with another person was usually enough to get the divorce granted. If we accept that we've moved past that, these laws are not of a concern. If fraudulent multiple marriage is a problem, then for plural marriage it should suffice to require that all persons involved in a plural marriage sign the certificate. So Charles would sign the certificate of marriage for Alex and Betty and Betty would also sign the certificate for Alex and Charles. Done.
Now we turn to more serious questions, which almost always revolve around money. Being married grants you access to certain monetary benefits, such as being able to be listed on your partner's insurance. Today in the US, we have a system where the price and reach of insurance is a somewhat market-driven phenomenon. I pay to list my wife on my workplace insurance and I pay (substantially) more to list my children. I see no reason I couldn't potentially list another partner, if I was willing to pay the price my employer and insurance company negotiate for it. We're already partway there with insurance plans that allow people to include so-called "other dependents" such as elderly relatives. We also control access to these benefits with a combination of market and government forces. For example, the ACA changed the age until which children could be covered on their parents' insurance.
Specific details aside, I believe that benefits controlled by private entities already come with prices and regulations about who can use them. If a plural partner wants to sign up for those benefits, there should be a price determined and restrictions set so they can see if they want to pay for it or not, and abide by the resulting restrictions or not.
In some cases a person might get certain government financial benefits; for example, access to reduced price items from a government-run store. The government already sets limits on who can access these benefits (e.g. adult children might be excluded) so I don't see it as terribly difficult for someone in a plural marriage to be likewise regulated.
Realistically plural marriages may end up generating revenue for governments just as the "marriage tax" - where in a married couple pays more income tax than two separate individuals - brings in more revenue. It's part of the deal and there's no reason that people in a plural marriage would automatically be a financial burden on anyone else.
And there lies the crux: in order to restrict a First Amendment right (the ability to speak and act as if married) the government needs to show a compelling interest. "It might cost some more money" is generally not such an interest, which leads me to conclude that the concept of plural marriage - polyamorous marriage with all consenting adults - is constitutional under the pre-Obergefell/post-Windsor interpretation of the US Constitution.
There is a whole "but what about the children" argument thread that is sometimes raised. Protection of children is indeed a compelling state interest. I have a hard time with this because "unfit parent" was part of the bigotry used against gay couples for so long and I don't think it should be a consideration in how marriage arrangements are regulated. That said, if anyone can produce evidence that having more adults around is somehow bad for children I'll consider it, but I've seen no such and seen anecdotal evidence to the contrary. People conveniently forget that this country had a centuries-long tradition of having other adults (uncles, spinster aunts, grandparents) in the same household helping care for children. If multiple adults voluntarily enter into an arrangement to care for and raise children I have a hard time seeing how that's a drawback.
I apologize for doing this piecemeal and at such length, but I think I've established that plural marriage ought to be legal under our current framework of laws and precedents without reaching for new rights. And that pleases me.