It's not going to be 32k lbs of towing... trust me. That's what it's advertised as but in reality you'll max out on payload long before you get to the 32k lb mark. If you calculate the real tow capacity based on a 5,300 lb payload (20% pin weight) that's a max tow weight of 26.5k.
This is all before you factor in things like cargo, people, a hitch, etc.. If you've got more than a 2wd tradesman model your payload is even lower than that. With something like a Laramie or a Limited, you're probably in the 4,700-4,800 lb payload range (23.5k actual tow capacity). Could even be slightly lower. That's almost 10k lbs less than advertised.
That's still good and plenty of payload to handle most things so don't get me wrong. It's just not what the advertisements say and a lot of people don't realize that. Anything that you change on the truck (such as tires) reduces the payload further. 500 lbs (your numbers) doesn't seem like a lot of payload to lose at 5,300 but if you lost that at 4,700 you're down into the 4,300 lb payload range. If you factor in 500 lbs of cargo, people, a hitch, etc... payload is now in the 3,800 lb range before you even hook a trailer to it.
If you're set on bigger tires, I would at least recommend that you make sure you're running the proper type of tire on the truck. I'd look for a load range E tire for sure. If you intend on changing wheels, make sure they're rated to handle the psi of the tires. Dually tires are capable of running much higher pressures (and you'll need it) for towing larger loads.