Now Let me first state that I am bisexual but I myself would not want to engage in polygamy simply because it is not my preference. However if all parties involved where to consent to the relationship fully aware that polygamy was involved I see no problem in it. Of course if not all parties are not in agreement the relationship should not be valid.
The problem is that laws are made based on morals and personal feelings while it should be based on whether or not anyone will be harmed because morals are subjective, for example in Somalia Female Genital Mutilation is morally fine, nothing wrong with it yet it isn't even considered in the US.
Now back to Polygamy, if everyone is consenting what is the problem with polygamy? No one is being harmed so why should it be illegal?
Whether someone marries a partner of the same sex or multiple partners, their choice of marriage is not going to affect anyone with seriously bad effects. Religion is not a reason to prohibit these choices because no religion has been proved true. If there are not any major negatives and people are happy doing this then let them, it's their life not ours.
To be honest, polygamous relationships as a general concept is very foreign to me, because while throughout my life I have encountered and interacted with many different forms of monogamous relationships between many different kinds of people, and because of this have become very familiar, oriented, and comfortable with monogamy, I have yet to personally interact with anyone in or that has been in a polygamous relationship, and I am somewhat socially conditioned to reject it based off of social folkways from where I was raised, so until I can physically meet and talk to a person in or previously in a relationship that was polygamous, I cannot actually adopt much more (or less) than a tepid neutral on the topic, and therefore, I do not support it, though that does not mean I am inherently against it either.