You may be a troll, but I think this is sort of important. In a further posting, the OP notes that the real deciding factor is consent. Consent is required for a marriage (and many other legal agreements). This is why, for example, I shouldn't be able to marry the Eiffel Tower: it is impossible for an inanimate object to offer consent. This is also a refutation of the common claim that allowing gay marriage inevitably leads to institutionalized bestiality. That's just a gross-out scare tactic. A dog or cat (or any other kind of animal) is not legally capable of consent, so there is no danger of codifying a relationship with an animal as 'marriage'.
So, this argument would seem to permit plural marriage. I don't have a problem with that. As long as all the people in a relationship are freely, understandingly consenting to their arrangement, what's the problem with that? Yes, it causes some trouble with things like spousal medical benefits and taxes and other things that are based on single-partner relationships, but I think we can come up with ways to deal with those problems.
There's kind of an idea in this country that we all know what marriage is, and it's this one particular thing. But is it, really? When we talk about 'protecting the institution of marriage', whose idea of the institution of marriage are we protecting? Many Catholics, for example, would say that there's really no such thing as a divorce; marriage is an eternal bond made before God, and when you swear that oath 'til death do you part, you don't get to change your mind, later. Still, about half of all marriages in the US end in divorce. It seems pretty silly for straight people to beat the 'sanctity of marriage' drum when they can't even get it right, themselves, half the time.
The real key, in my mind, is to disassociate the legal agreement of marriage with the religious ceremony of marriage. I don't see any special reason why religious marriage should be recognized as a special institution by the government. Civil marriage contracts should be required for legal purposes, and should only be potentially coincidental to religious marriage. Why did we make the Mormons give up plural marriage? Their religion defined it as acceptable, but the majority religion in the US did not. For a country that supposedly separated church and state, we have some pretty suspiciously Christian rules in place.
p.s. - I realize that many 'plural marriages' today are little more than excuses for disgusting men to have sex with a lot of young girls. That's not really a plural marriage, at all, because informed consent and freedom to dissolve the contract are completely absent from those situations. I absolutely don't support the practice of enslaving young girls and calling it 'marriage'.