I don't think there is much regulation up there at all. They ask that you camp in designated sites, but many people weren't. Nobody came by and said anything. I didn't see anything specifying a maximum number of people per site or any limitations to the number of sites a group could occupy. The sites near the canyon would not fit more than 2-3 cars. Our site fit my truck and 41' fifth wheel without any room for additional vehicles. But our site easily had room for 3-4 tents. So you could perhaps park off the road in different spots and then walk to the campsite, which would be easy to do.
Perhaps the sites farther away from actual canyon are larger. I don't know because we didn't go down that way.