We've found state parks to be more forgiving on the amount of people, and usually have MUCH larger campsites. In Connecticut at least you probably won't have electric or water connections but bath houses are common, and sitting around a campfire requires no electricity.
When we've "dry camped" (no hookups) usually only Mom and Dad get to use the camper's bathroom while everyone else uses the campgrounds bath houses. With careful use and a strict policy of "shut it off!" the camper's battery easily lasts a weekend - and we've stretched that to a week with a brand new battery.
For a few years we camped with up to 3 other families. Tried to get adjoining campsites and then would sort of set up a "compound" to gather and eat. A LOT of fun!
If you search around you will be able to find more affordable camping opportunities. Also, ASK when you make reservations about any extra costs with a lot of people. Sure, a lot of campgrounds don't necessarily enforce all of their rules (ESPECIALLY if your group is polite and quiet!), but you don't want to run into any issues in the middle of a camping trip.