Polyamory Next?

Will Christian churches actually come under internal pressure to bless polyamorous unions?

Suppose, contrary to facts as they stand, that secular American society ended up legally recognizing polyamorous unions, so that one could go to a justice of the peace and have one's polyamorous union given legal standing by civil authorities. What should the Church do, as a matter of general policy, in such a case?

One would hope the Church has by that time developed a better theological understanding of marriage, so that it can render intelligible, if not persuasive, to civil society whatever it ends up doing. I would hope the Church could mount a convincing defense of--how shall we call it?--binary marriage unions, and this is what it would likely do.

But why? What makes binary rather than polyamorous unions so special? Can we say anything persuasive? Suppose the Christian polyamorist argued:

(1) The Bible supports unions exhibiting fruits of the Spirit;
(2) The Church is permitted to bless unions that the Bible supports;
(3) Some polyamorous unions exhibit fruits of the Spirit;
Thus, (4) the Church is permitted to bless those polyamorous unions that exhibit fruits of the Spirit.

Will GC resolutions follow on (4)? What's wrong with that argument? Or do you think that anything is wrong with it? I have some ideas about what's wrong with it that I'll share in a bit, but I wanted first to ask the question.