As far as I know, bigamy is illegal (and you can be prosecuted for it) anywhere in USA.
Now, imagine that a polyamorous trouplethrouple (3 people in a relationship) is formed, and acts, in perfect unison (e.g. all 3 move in together on the same day, etc...), and all 3 members act in a way which fits fully into a state's common-law marriage rules.
In that case, can the 3 participants be prosecuted for bigamy? Because technically, every one of the three, is in a provable common-law marriage with two people at the same time.
Please note that this can't be "lawyered out of" by arguing that one of the two "common law" marriages is invalid because it was entered into later; since everything all 3 do is in synchrony, at the same time. Either all 3 are common-law married, or none of them is, unless somehow the law says you can roll dice and arbitrarily pick 2 people out of 3 and their bond is a valid common-law marriage and the other two sides of the triangle aren't valid with no tangible reason for why.