Then legalize same sex marriage, dummy

[Lemur]

However, if marriage is NOT confined to a one man-one woman definition, why would a polyandrous or polygamous marriage be still be preventable [...]? On what grounds can such a union be denied?

On the grounds that there is no popular or political support for such a change. The law is not an abstract exercise in logic, but rather a clumsy, ham-handed attempt to regulate the affairs of citizens. (Emphasis on "attempt.") Look, Seamus, you've heard the expression that, "A cult is a religion with no political power," right? I would apply that maxim here. A variation on marriage with no political or popular will behind it is marginal, and shall remain so until conditions change. (E.G., we all knew that marriage between blacks and whites was an illegal abomination, until we collectively realized it wasn't. Likewise, we all knew gays were wicked pedophiles who could never marry, until one day ....)

One can theorize all one likes about "if we treat X then we must allow Y," but at the end of the day, you're gonna need that argument and (much more importantly) about nine bucks to get a Denny's Grand Slam Breakfast.

Would poly matter if all are consenting [...] adults?

Our body of law is not set up to handle this sort of arrangement. Consider inheritance. Consider benefits. Consider custody. Consider all of the ways a family can disintegrate, and all of the props and stop-gaps we have set up to manage these events. All can be applied to a same-sex couple with low to no work. Almost none can be applied to a hippie commune in Oregon where eight people married each other. Our body of family law would need to be amended or rewritten from the ground up.

Like I said, big ol' can of worms.