Marriage, from a legal perspective, is a contract. There are some specific things that apply solely to the marriage contract, and they can be interpreted differently depending on what state you're in. For instance, in most places, the child born of a married woman is automatically considered to be the child of the husband. Unless he can prove otherwise, he's on the hook for that kid until it's 18. This doesn't change if the child is raised in a family of two women, or adopted into a family of two men. The 'spouse' is on the hook. But what happens in a family of multiple wives? Are the other wives on the hook for each other's kids? What if one wants to divorce, do the other wives get custody rights? Do the parents of the other wives get "grandparents rights"? Although rarer in human culture, what happens in a family of multiple males? Do the dad's just decide who gets to be the presumptive "father" of the kid (notably, in Nepal where this is still practiced to a small extent, the mother says who the father is and everyone just agrees that she is right)? Is it all left to genetic testing? Or is everyone just on the hook as if they all adopted it? How is that sharing parcelled out?
Now let's talk about inheritance. Generally, when you die, your assets go to your spouse or, in their absence to your children in equal portions. Now of course, anyone can make a will and give everything to their beloved parakeet if they so desire, but what we're talking about is probate and how things are split up intestate. In a polygamous/polyandros marriage do the spouses share equally? Is the spouse that's been married longer accorded more assets? What about the children from each, how do they share? More laws would need to be written.
Then you get into some really weird stuff. A lot of states still criminalize adultery. Now if one man has two wives, but the wives aren't married to each other (perhaps because there's no gay marriage), does that mean the man is criminally adulterous when making love to either of them? Is it okay if all three are involved in the act?
These are hard questions to answer, but more important, the way they would be answered is by having each and every one result in a brand new law. Each and every state would attempt to do their laws differently, and there would be challenges to all the laws at the state and federal level. In other words, it would be a pain in the butt.
Our current legal system is made to deal with two partner unions. It has enough trouble dealing when those two partners separate and/or find new partners. Conversely, our legal system (save in those states that have specifically enacted anti-gay-marriage laws) doesn't segregate people by sex. Ultimately, not much need be changed by instituting laws making gay marriage/civil unions legal.
As a rights thing, it's more difficult to argue against multplicity in marriage (as the devout Mormon in my law school class could tell you). I personally don't have a huge problem with it (as long as there's no abuse going on). I wouldn't mind having another husband!