I have to echo the sentiments of Jude and Trieste. I, like many others here, have no issue with polyamory and any variety of open relationship, however it's the legality of entitlements, insurance, and inheritance that seem an impossible tangle. Such things are complicated enough with ex-spouses and children by multiple couplings. Would child paternity need to be confirmed via DNA with every birth? How would the law handle, for instance, if A is married to B, C, and D, and D is married to E who is married to F. If D dies, who has rights to D's assets? D's children? D's entitlements? A and E? Would F get any share? What about D's sibling spouses?
Also, unlike marriage between homosexuals, I don't think the majority would demand such a right, as a few have pointed out the unpopularity of the concept based on negative attitudes toward the religious groups who have practiced it or based our culture's seeming monogamy-normative morals (regardless of popular habits). I say let any adult bed, love, and share their lives with any other consenting adult(s), but, legally, I don't think the law could handle the tangled weave of polygamy.