Group sites. Look for a place that offers group sites. Some also sometimes have paired sites, that is, a site with dual facilities intended for two "especially close" families. I volunteer at an NFS campground that has both two group areas and among the "regular" sites, a couple "paired" sites. And while we try to welcome and accommodate everyone, the fact remains that the facilities do impose limitations on us all. And a group of 9 or 10 is going to use more resources than a group of 4.
Other posters have enumerated the reasons for such limitations. There's no telling which specific reasons are at play in any given campground, but probably all of them to a greater or lesser degree.