What can a Ram 3500 (6.7 Cummins DRW, gooseneck) ('13-18) actually tow?

The rating is the easy half of the answer. A trailer never weighs its brochure dry weight — water is 8.34 lb a gallon, propane and batteries ride along, and so does your gear — and hundreds of models changed their published weights mid-run, so the model year decides as much as the model. Judged that way, with a 10% margin and 2 people aboard: 5150 of 5150 campers fit a Ram 3500 (6.7 Cummins DRW, gooseneck).

The number that quietly binds is payload — 6,580 lb (Regular Cab 4x2 DRW, 6.7 Cummins HO / AS69RC, 4.10 axle, 14,000-lb GVWR, 39,100 GCWR - the exact row rated 31,210 lb): tongue weight lands on the rear axle with your passengers and the hitch, so a vehicle often runs out of payload well before it runs out of rating.