Would it be possible to make a 2013 Tahoe to be able to pull more from the tongue than it already can? If so what mods or upgrades would be needed?
I can’t tell for sure what you’re asking - how to make the hitch stronger or how to make the Tahoe a more capable towing rig.
The hitch itself is rated for 6000 pounds without a weight distributing hitch attached to it, or 10000 pounds with one. But the hitch isn’t the limiting factor. Towing capacity for the vehicle is around 8000 pounds, depending on how it’s configured, and it will pull it but it won’t be happy about it. In the summer you’ll run into engine and transmission temp issues, and you’ll also run into durability issues with the transmission and rear differential. The 5.3 is also underpowered for towing near the limits.
The towing capacity of the vehicle is just one of several numerical limits. Another is payload capacity (yellow sticker in the door jamb), and front/rear axle capacity. I’ll spare you the details on these and assume you know where to find that out. I’ll also assume that you’re just looking for practical steps you can take to make the truck a better towing rig while staying within the legal and manufacturer’s stated limits.
I tow a 7000 lb camper with a 2012 Yukon XL Denali with the 6.2L engine, 6L80E transmission and 3.42 rear axle ratio. I’ve had to install a larger radiator, a better transmission cooler setup, a billet torque converter in the transmission, and am planning to upgrade the rear axle to a 14-bolt 3.42 unit from a 2WD Escalade. I’ve also put in a bigger cam designed for towing that boosts both horsepower and torque. All of these mods were to address specific weak points and improve long term durability and reliability while towing. The cam was mainly to improve performance.
Your Tahoe will do just fine towing up to about 5000 pounds without any mods, and still stay cool. It’s when you start getting close to the towing capacity of the truck that you will start having cooling and potentially durability problems - especially in the summer. Even at that, you’re going to be living on borrowed time with the factory torque converter beyond 120k miles and towing.