Last year, I got greedy. Well, that and I was trying pumpkins for the first time in a gazillion years, and I hadn't a clue what I was doing. I was up to 21 viable pumpkins for three plants, just the small kind, and the plants started to selectively abort the excess. I think I wound up with 18. I decided that pumpkins will step in and take care of themselves. If they decide they can't support all the pumpkins on the vine, they will kill some to make certain the others live.
I also found that the more each plant produced, the smaller were the pumpkins. Some of the ones I processed at the end were quite puny for the variety of I was growing. I think that's especially true with the giants, which I've never tried. I've read, though, that you want to limit them to two per plant, maybe even one, to get the big ones.
"Imagination is more important than knowledge." -- Albert Einstein