You've described (traditional) polygamy. All polygamy is polyamory, but not all polyamory is polygamy. Polyamory in and of itself doesn't have set restrictions and rules to the relationships that are established; some polyamarous relationships are bigamous (which is sort of what I'm describing), where people are married to two or more people within a polyamarous relationship.
And seeing as how most polyamarous relationships exist within the context of religious practice/theistic cultural practice, I think in secular state like America, most of the formalities that exist in traditional polygamy wouldn't apply. Also, things like homosexuality, and open sexual promiscuity aren't accounted for in traditional polygamy, so you could see a polyamarous relationship where there are 2 husbands and 1 wife, or 3 husbands, or 3 wives, where each member of the relationship are married to one another individuality. It was Fountain who set the limit of 3 members in his thread as well, and I personally believe there wouldn't be a limit to the amount of members permitted to exist within a polyamarous marriage, because there's no argument you could present against setting a limit once you accept surpassing the natural limit of 2. I could maybe see legal limitations and statutes being putting place limiting the amount of people you could marry (ex. you can have more than 10 husbands in the State of X), but on an abstract level, there really isn't much you can do once you've accepted polyamory on principle.
I don't think people would start going out there and marrying 50 people at a time, but it doesn't need to go to that extreme for things to be in arrive at a state of complete and utter chaos.