The Green Mountain Club asks that groups limit their size to 10 for any backpacking trips. I can't remember the ADK's group size limit. In the GMC's case, they're just pushing a Green Mountain National Forest rule that otherwise goes unenforced.
I think AMC has a similar rule, but I'm reminded of a time when I was coming down from Madison Hut and saw a single group of over fifty people going up for a night there. It was raining, so I was focused on my feet rather than the trail ahead, and they saw me first. Before I could say anything, their group leader called back to the group to let me pass. Fifty people stepped off the trail and into the bushes on the side. Good manners, but I would have much rather stepped off the trail myself to let them pass and only had one person trampling the undergrowth and soil on the edge of the trail, rather than fifty.
Made me wonder-- the people at AMC's reservations center must know about the group size limit, but when a group of fifty is about to pay for a night at a hut, do the dollar signs in their eyes make them forget to mention it? Or, like I've seen on the LT, is it just impossible to convince people to split the group up a bit?