Limit of six people per site?

Are you looking at commercial or USFS CG?

Many USFS CG (as well as National Parks) have group sites, specifically for such situations. Nearly every place I've seen or been to, at least here in Colorado, have a 6-8 person limit/site. No explanation as to why, just that limit. But with the option of a group site, usually in a seperate or different loop, with a higher limit.

If you're looking at commercial, I'm sure some of the park owners that are on the forum could give a good reason as to why a 6 person limit.

imagine every campsite occupied with 10 people each. It's that scenario that the max limit is established. It's conceivable that a group or organization would reserve several spots co-located and max out the spots with 10 people, overloading the facilities as well as disrupt the other campers.
So just reserve two spots, stretch out and enjoy!
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It may well be fire codes, or similar restrictions. Government regulations do not always make logical sense.

In some cases I think it has to do with sanitary codes; the sewage system and bath houses are sized for a certain number of people, figured at x per site, and they're not permitted to have more than that per site. I think in most cases it's just the management (be it public or private) not wanting to overcrowd sites and to avoid problems with rowdiness, excess noise, etc.

Perhaps you can book two adjacent sites, maybe putting a tent on the other one if they require some structure there.

I recall a funny story here posted not too long ago about a larger party camping together over two campsites and a rather disagreeable ranger. They were eating dinner at the picnic table (all in one campsite), and the ranger informed them that it was too many people on the one site and some of them would have to move to the other site. Undeterred, they picked up the two picnic tables, put them side-by-side at the boundary line between the campsites, and continued their dinner. The ranger was not amused at this solution, but couldn't do anything about it, particularly as all the other campers were enjoying his discomfit. I wish I could find that thread....