It isn't clear to me what the purpose of such a legally recognized partnership would be. All the functions of legal inter-human marriage that I can think of are inapplicable. Humans already have the rights to do anything they want to their pets. Giving rights to pets is pointless if they can't effectively claim them (deciding on partner's treatment in a medical emergency, custody of partner's body after death). Tax and property rights - non-humans can't own property or money. Custody of children is irrelevant. Etc.
A thought occurred to me today as I skimmed an article in a rationality forum where the subject of gay marriage cropped up; seeing as the issue has been hotly contested in various public fora and especially the courts, what about poly? After all, many if not all the arguments for gay marriage apply to poly marriage as well.
Questions for LWers who are currently in a such a relationship, or have an opinion to share:
Do polies want to marry each other or do such relationships not lend themselves to permanence above a threshold of partners? Should polies campaign for the right for a civil union anyway? what are the up and down sides of this? etc