The most overlooked limitation is the brake duty cycle. The brakes convert kinetic energy to heat energy. They are rated for a certain overall weight. If you're trying to stop extra payload, especially in an emergency situation or downhill, the brake disks will overheat and fade (stop working). Other components that are designed to meet an OEM payload rating are the axle bearings, transmission and drivetrain, and cooling capacity.
If the truck is designed to tow, then I wonder what the assumption is for trailer brakes? For example, the 2018 Tacoma is designed for up to 6400 lb trailer. Definitely the transmission, cooling and drive train can handle big loads. Not the axle bearings though.
I've rationalized the engine and brakes are ok for being a few hundred pounds overweight (about 10%). And things like axle, tires, frame, etc. have more than 10% excess fatigue life which is probably what will fail before ultimate strength. The brakes, engine and drivetrain should be ok. I know commercial airplanes are designed for 50% ultimate strength above maximum design load, but have no idea what trucks are designed for. I'd guess a lot higher than 50% because weight isn't such a big deal. Airplanes are designed for about 4 times fatigue life (about 20 years). Landing gear has different design constraints, having to do with "safe life" which is more than I can explain but involves a bunch of testing.