Polygamy as it's commonly practiced in religious groups in the US really is about oppression and subjugation of women, and this naturally extends to the children in the clan. The relationship whereby one man has exclusive sexual rights over a number of women both illustrates and reinforces the power relationship that underlies the whole arrangement.
Hence my modest solution: Polygamy of any flavor (polygyny, polyandry, group marriage) should be allowed and even legally recognized so long as everyone in the relationship has at least two sexual partners in the group. This automatically flattens the power structure and puts everybody onto a more equal footing. Imagine a situation where one man has two wives. If the two women are also doing the horizontal tango between themselves, it goes a long way toward dethroning the man as "head of the clan." And, knocked from his patriarchal pedestal, the fellow might possibly fall straight into the sack for a steamy menage a trois, democratizing things even more explicitly. Anyway, you get the idea....
