It might be possible, but probably not. The axle ratio is out there in the specs, but really makes no sense. The 8-speed transmission has a 4.71 first gear, so having enough torque to get moving should never be an issue. I'm not sure what prompted FCA to make such a big distinction based on axle ratio. Ford drops capacity 1/2 as much.
However, even the 3.92 tested with the J2807 specs has a 17,000 lb GCVW. That would mean your truck, passengers, cargo, and the hitch would need to be under 6000. It is possible to achieve that, but it means a truck with few options and limited cargo. An 8000 lb-10,000 lb trailer is a more practical maximum weight. In most Ram 1500s that could still challenge GAWR and GVWR, requiring some of the mods below.
There are a couple of long threads about how GVWR and GAWR are determined and if they can be modified. There are also discussions on tongue weight. This is one:
https://5thgenrams.com/community/th...etermine-max-payload-and-towing-weight.13097/. There are both engineering and legal issues, the legal issues varying by jurisdiction. My call would be yes, you can raise the rear GAWR and de facto GVWR (which is just a SWAG anyway). However, you are looking at a combination of an increase in spring rate (supplemental air springs, stiffer coil springs, and/or Timbren rubber springs), wheels with higher capacity, and LT tires with higher capacity. Note that a truck used commercially or in some jurisdictions (including most of Canada) would be judged by the GVWR on the door jam and possibly subject to a significant fine.
If it is a bumper-pull trailer it will need a WD hitch. That alone reduces the tongue weight, transferring weight to the trailer axle. However, I believe and at least one WD hitch manufacturer has told me that the tongue weight should be 4.5%-5.5% after WD adjustment, which probably means about 6% before adjustment. So, if it is a bumper-pull, you will probably be ok from a payload standpoint without increasing GAWR or GVWR. But the GCWR could still be a concern. Note that some trailers are designed for 10% or greater tongue weight and don't have enough flexibility to reduce it.
The advertised towing and payload numbers are for the lightest model with no options. It is less in the real world.
Is the trailer really 11,000 lb or is that it's GVWR?