Depends. How big of a family do you have? What do they weigh? how much payload is left after the family, dog, in my case the rack for the canoe, generator, cross bed tool box etc. My 96 CC 9200 gvwr rig had all of 600-700 lbs of payload left of 2400 for trailer hitch wt. I would have overloaded my truck with the trailer the op is looking at.
There is more to what is a safe tow setup than tow ratings only!
Marty
92 Navistar dump truck, 7.3L 7 sp, 4.33 gears with a Detroit no spin
2014 Chevy 1500 Dual cab 4x4
92 Red-e-haul 12K equipment trailer