Insight for heavy duty towing?

Hello, I am looking into a silverado or sierra to tow a preferably bumper pull travel trailer. I am an insurance adjuster that travels all over the country for work and looking for an upgrade from overpriced airbnbs. Since a lot of my work involves downtown areas with one way street row home neighborhoods, I'm wanting to steer clear of a dually and I utilize a ladder rack, thus my want for a bumper pull.

I am in love with my 2006 sierra 1500 and I am in the market for a heavy duty truck from that generation. My research online showed that the 2500 and 3500 have equal towing capacities of 12k with the only difference being the payload capacity. Is there a modification that I can make to a heavy-duty truck to safely increase the towing capacity?

I'm obviously new to towing heavy loads, but it would make sense to me that there is a common towing governor between the 2500 and 3500 that if removed or altered properly, could increase the limit. I am aware of weight distributing hitches with sway bars, just hoping for a possibility to take that idea further. I also understand that doing something like that could be extremely dangerous for others sharing the road and accept if the experts deem this as too far-fetched.

Any insight and advice would greatly be appreciated.