There are some larger motorhomes out there with a bigger payload than you might expect.
We had to give it a lot of consideration when buying ours as I can only drive up to 3.5 ton, so it took us a fair bit of time finding something that was suitable for us as a family (2 Adults, 2 Kids, 1 Dog) with a reasonable payload and the right layout etc.
We eventually found a six berth, twin axle Dethleffs which is a wonderful vehicle for us with rear bunks and an over cab bed.
Last time we weighed it with all of us on board, a full tank of fuel and everything we needed for a week away it came in at 3480kg. The only thing we don’t have on it which most might consider a standard fitting is an awning. If we did have one it would clearly take us over the limit given they are pretty heavy but we would never use it anyway so no loss to us really.