As father to three children, my experience is that you only think two is exponentially more complex than one. At least with two, they don't always outnumber you!
With a simplifying assumption of only pairs of siblings getting into fights, its C(n,2) which is 0,1,3,6,10,15 for 1-6 kids. I have a friend with 6 kids and can confirm that there are roughly 15x as many fights between the siblings as friends with 2 kids. Age differences do matter though (if your kids are much more than about 10 years apart, they tend to clash a bit less because they are less in competition with each other).