This is simply polygamy marriage, isn’t it? The Muslims do it. The old-style Mormons did it. Heck, the Old Testament is full of people with many wives. I’m really not into such thing, but this is not new at all.
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.
The difference is that in polygamy the women are both married to the man, but not to each other. So it’s still between “a man and a woman”, it’s just that the man has two marriages at the same time.