I believe that as along as all parties involved are honest with each other and open about what they expect from the beginning this is a wonder lifestyle so why shouldn't it be legal? I am not saying crazy ass people who are marrying children or doing it to have sex with everyone they can but people who are truly doing it for the right reasons.
The problem is with insurance benefits, child support, inheritance and the like. While I see no problems with it being practiced it should not be legally acknowledged for economic reasons. What if a soldier who is the husband of two is killed? The government can't split the money payed out in half because both spouses would have to little, but then again paying twice the cash is unacceptable too. How could a company offer insurance benefits to the family of someone with 20 wives? How do you administer cases with a marriage decagon of 6 men and 4 women? What do you do with people exploiting the system for money?