Ed T's original question was about the need for *laws* regarding multiple marriages of any sort. That is a bit different than questioning multiple relationships in general.

There are obviously many issues when people try to interact 'intimately' in more complex ways. Human psychology makes even monogamy sometimes difficult, and with 3..or 4.. or communes... the odds of problems arising increase geometrically. A major one, simply stated, is that although it may be possible to 'love' more than one partner, it is not possible to give multiple partners all the time & attention that they may desire. Thus, issues of fairness and favoritism may arise.
All of this of course depends on the specific compatibilities and 'comfort levels' of the various individuals. I have no doubt that quite successful multiple relationships do happen... even without formal marriage. But I also suspect that most of those make an effort to keep a low profile... possibly by living in a secluded area that doesn't attract neighbors' attention.

All these issues were explored back in the Naughty 60s when 'hippies' and 'free love' were big news, and one author, Robert Rimmer, wrote several novels on the topic(s). Notably, "The Rebellion of Yale Marrat", "The Harrad Experiment" and "Proposition 31"...but also a number of other books.

'Harrad' & Proposition 31 followed a group of kids from 'experimenting' in college to trying to maintain a residence after graduating... with the usual issues of getting along together added to their public problems with law & society. (In Prop 31, one person argues for maintaining as much anonymity as possible, while another favors daring the world to accept them.)

Now...as to the law. IF one wants to argue, as this group in Montana does, that the law should allow polygamy.. or any other multiple situation.. they must realize that any law(s) will have to deal with all the complexities of finances, inheritance, child rearing, divorce, and even residential zoning.
   I would suggest that it all 'might' be possible if a special bureaucracy and court were established, requiring any group wishing to 'go legal' to submit a detailed plan as to rights and responsibilities. This would have to be examined for conflicts with OTHER laws, as well as internal consistency before any license were issued. (You can see that just designing the legal forms might give rise to an entire new branch of lawyers!) It is no wonder that no state wants to get into the technicalities, much less the moralities, of the issue.

There have been various societies in history where polygamy, polyandry etc. were legal and/or ignored, but very seldom has human psychology managed to make this a smoothly administered situation. This guy in Montana may or may not be honest about his motives... and his 'wives' may or may not be equally comfortable with the arrangement... but I suspect they are facing defeat in the long run. Better just shut up and enjoy it as long as everyone is getting along ok.