I have read a few things on polygamy in the Bible before. I am an atheist, so take what I say with a grain of salt. Basically, I was in a debate with a Christian on gay marriage. Their stance was that God defined marriage as one man and one woman. So I went looking through the Bible to see if that really had support.
Roughly, what I found was that polygyny was pretty common and seems to be Bibilically supported. As pointed out in this thread, there are many instances of polygyny in the Bible.
The Christian I debated said it was like divorce. It was something there, but not preferred. However, there are places where it says that God gave multiple wives to certain people. God did not consider David's multiple wives to be adultery (because he was punished for adultery later on). So it seemed pretty clear that God approved and even helped out.
There was a mention of "one flesh" to justify monogamy. However, I found "one flesh" to be a euphemism for sex since it talkes about a man being "one flesh" with a prostitute later on.
The Christian pointed out that God said that there should not be multiple wives in one passage. But when I looked it up, that passage only applied to kings and the meaning was "not too many wives."
One of the problems is that TheRainKing quotes Matthew 5: "17"Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished." This has been a very sticky point. Since heaven and earth have not disappeared, the Old Testament laws should be in effect. But no one really wants to follow these Old Laws since it would involve horrible stuff like killing girls who had premaritial sex in front of their parents. Or making raped women marry their rapist. Or stoning homosexuals.
Many Christians get around this by ignoring this; saying "heaven and earth disappearing" means something else; say that the laws are in effect but just for Jews; or some other means. I have only met very few Christians who really want to follow the Old Testament. Unfortunately, many Christians have a salad bar approach to following the Old Testament. Maybe a few of the Ten Commandments and a few other laws they may like, but ignore the rest.
All in all, I think it is easier for a Christian to ignore the Old Testament laws and focus more on the New Testament. It is very hard to support polyamory with Old Testament laws unless you are justifying polygyny. I think polyamory gets more support from the New Testament's idea of love.
Anyway, just my 2 cents.