can I increase my tow vehicle's tow rating

Some will have optional gear ratios that will give you maybe 1000/2000 pounds increase. Payload however does not improve.

Much depends on the tow vehicle.
If its a small V8 or V6 1/2 ton size vehicle/suv/van/etc the vehicles frame/brakes/trannies are close to maxed out using the mfg tow rating.
Other vehicles like a new gen 3/4 ton diesel are the most under rated vehicle out here....mostly because of low 6000-6500 RAWR. These trucks may have the same engine/frame/brakes/tranny front and rear axles/etc as the 3500 SRW trucks ( example Fords F250 with the camper package or heavy service pack).
Of course this doesn't change the mfg tow rating.

“can I increase my tow vehicle's tow rating”

No! The manufacturer built the TV and set the rating.

Manufacturers use many things to calculate tow ratings. Some of them are engines, transmissions, tires, brakes, frames, suspensions, and hitch classes. In addition to tow weight rating, the vehicle has a rating for it's max weight, a rating for the weight it can carry, and your hitch receiver has ratings for what it can carry. All of those ratings are tied together.

Nothing you do to the vehicle can change it's ratings. Increasing engine performance might help you accelerate faster, but, it would do nothing as far as carrying weight, and if the engine performance upgrades added any weight to the vehicle, it would actually reduce towing capacity.

Note: When you see advertised manufacturer tow ratings , they say this vehicle can tow up to XXXX lbs. Then the fine print in their owners manual says "the vehicles tow rating does not include passengers or cargo". When you add these to the vehicle, it's tow rating is reduced, pound for pound". Different options also affect tow capacity. Side by side vehicles with same engine, frame, brakes, etc, one has two wheel drive and the other has four wheel drive, the two wheel drive will have higher tow capacity, because it weighs less.