Polygamy is therefore rationally ordered to the social purposes of marriage, namely, the identification of the mother and father of a child, and the reciprocal responsibilities thereof. Polygamy still binds together the social, economic, legal and genetic aspects of father and mother into a unity, for the sake of the offspring.
Polyamory --- at least as I understand it --- posits a spousal relation betwen the women, as well as between each woman and the man. Therefore it veers away from the procreative form, which is the only rational public purpose for marriage to begin with.
Any other kind of agreement can be a private contract. That's what contracts are for.
Arrangement regarding familial roles can arise to their needs, just like in polygamy societies. In some society, the kin line follows both sides (bilineal) so that matters such as inheritance, care for the elderly, etc., are done through discretion of the parties involved.