Marriage definitions invite slippery slope arguments, so I think it's worth explaining why, even if we grant that non-straight marriage is on a slope, that it's not slippery -- that the reasons to support non-straight marriages are not applicable to further undesired redefinitions of marriage.
I prefer to define marriage as a union entered by two consenting and competent people. Obviously "consent" and "competence" rule out most of the man-bites-dog/dog-marries-man's sister scenarios, child marriages and the like so the word that I will try to justify is "two."
One difference between two people and three is that two can have discussions but not debates. A "debate" happens when remarks are directed at a third-party, not at the person who is expected to respond. Two's company, three's a political entity.
Given this difference we can construct an attack scenario that shows why someone who supports gay marriage can provide good reason not to extend that to arbitrary other marriages.
The US 5th Amendment does not specifically include it, but Common Law includes "Spousal Privilege" which holds that one cannot be compelled to testify against one's spouse, and allows one spouse to exclude a spouse's (or ex-'s) testimony from being used against them (modulo court disputes between spouses). Most communication between spouses is considered privileged communication similar to that between a lawyer and their client.
One positive reason not to expand the definition of marriage to three or more people is to prevent spousal privilege from being used by groups of criminal conspirators. If people in a relatively small but powerful corporation like a hedge fund all married each other, they could then act secure in the knowledge that no investigator could offer deals to flip a low-level defendant against the high-level defendants because the resulting testimony would be inadmissible due to spousal privilege.
Where Mafias have to choose between close loyalty ties that limit risk or recruiting diverse talents for their criminal conspiracies; corporatization of marriage would limit risk while allowing relatively easy recruitment into the criminal conspiracy.
To be clear, I am not against any and all recognition of plural relationships but am against extending common law spousal privilege to them.