'Our system is messy and complicated, so if we add more variables, it will be an even bigger mess!' - so make the system less messy and enable more variables.
Can you imagine if someone came and said add this function/feature to the program and in response you said "the program is complicated and the code is long, no need to confound it any further with features."
Vague metaphors aside, this happens occasionally in the industry I'm in (finance) when we trade small lots of non-traditional products. These products don't follow many of the rules that all of our other traded products do. Instead of re-writing our systems to deal with these(totally impractical), we manually shimmy these in to the database until they expire or are traded away, at which point we can forget about them.
I don't see what would change such that it would introduce any new complexity on that side of things.
The exact same complexity already exists today: step-parents. It's mostly a non-issue and is well defined. Step parents acquire no custody rights over the child inherently. If my wife remarries, and we had a child together, the parental rights are retained in myself and her. The same would be the case in a three-way break away on that ten person marriage; there would be (in this scenario) a two person custody of the child, eg the biological parents.
Again, I'm not saying this argument is valid or should carry the day, only that it is defensible and non-bigoted.
Nothing changes about the legal custody system of children due to N-way marriages.
If two people in the N-way marriage have a child, it's not the N-way marriage that acquires custody, it's the two biological parents.
Marriages do not define custody, period. That is not how it works in the US.
Keep in mind that presumptively is not definitively. If there is a paternity test that later says otherwise, eg if your wife or husband cheated on you, then that other person can typically acquire parental custody, because they are the biological parent. All things being equal (not involving abuse or danger to the child), biology is the first line of legal custody.
What about adoption? The most sane thing to do near-term, would be to keep it the same - adoptions are max two people legal scenarios. If the system is cleaned up, simplified, or otherwise adjusted for N-way marriages, then perhaps later there could be N-way adoptions as well (and scientifically, we may eventually see N-way biological custody too).