I think it would make more sense for there to be couple marriages. As in, rather than all three people getting married in one big union, have three different contracts. This way, one person can marry two later on rather than all of them needing to get married at the same time, and if someone breaks up with one person but not the other, only the relevant union would be broken.
I'm not sure if they would put a limit. It might make sense, to make sure the marriages aren't sham marriages, that they're love marriages. Could be a maximum of, say, one ceremony per year/ per two years or something, with each person being allowed to marry only up to 2 or 3 people per ceremony? I don't know how that could work but that might prevent the forced marriages or reduce their occurrence.
Or just being more careful in a second marriage, before the ceremony. To get Canadian residency I've been having to prove I have a real relationship with Ragabash, I can imagine something like that being decided.
Also I can very well imagine that any prior spouse would have to give their consent, too. They need to make sure you can't get married to several people in secret and lead a double or triple life.
I don't know how it would work for taxes, but there are lots of cases with dependents (kids, disabled relatives, etc) that work even with more than one person at a time, so it sounds like it should be doable to file taxes all together. For health insurance, I can imagine paying more if you want more people to be covered by it, although in many cases each spouse might just have their own coverage, too.
Polygamous divorces would really be the pain. What belongs to every spouse? Take my case, say I'm married to Rag and get married to Sean, and they're not married to one another. I get a divorce with one of them. What the other earned is half mine, but shouldn't be theirs at all... How do we calculate it? What about purchases made with the three of us, does the man divorcing me get a third of them?
Seems like it has potential to be messy, and then if you add kids to the mix... it's even more complicated. I assume the biological parents would be given priority, but if three people raise a child together, it seems fair to say they're all parents. If the third one, who didn't conceive the child, gets a divorce, they should get some rights over the kids, visitation rights or something.
I should probably stop here, I can see lots of issues. This being said, there are lots of complicated cases with blended families as well I assume so that shouldn't mean it's impossible.