I'm not an expert, but you shouldn't have to do anything with the transmission to my knowledge. Some smaller sedans can have transmission issues when you put big rims on, but the escalade should be fine. You may have speedometer issues, but I doubt that as well. Maybe if you were going a bit bigger, but you should be good with the 24s.
I'm not an expert either but I think it has to do with wheel size and tire size for example on my 05 esv I've not had to tune my cars speedometer but the wheels I have are different sizes. My winter tires are 265/70/R17s I believe and my main tires are 305/45/R22s.
Although I do know this info that the first number means total rim and tire size then the middle means tire ratio and the last number with "R" is Tim size. So on my winter tires they are 17s.
The real issue is the overall tire size diameter compared to stock. If it is exactly the same, all is well. If the new tire/wheel is taller than stock, there is a bunch of issues. The speedometer will run slower (whatever it reads, you will be going faster), it will have an effect on your ABS brakes system, it will change your final drive ratio so that it feels like you have lost power.
I switched my 17s to 18s but made absolutely sure the 18 had lower profile tires so that the overall diameter was the same, and had no problems.
Automobile(s): 2015.5 black premium, sold my black 2003 ESV
London, Ontario, Canada, 11450
Re: 24s on the caddy
I put 24's on mine, when turning, the tire rubbed the plastic fender lining a bit.
I grabbed the drill and some zip ties to pull the fender lining away from where the wheel was rubbing it.
I had to trim the bottom of the plastic windshield washer resovoir a bit for clearance.
Total time was about 15 minutes.
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It's dark so I had to hit the led's, but you can see how mutch room you have with 305/35/24.. But regardless no rubbing the ride is crap. Truck rides like a hay wagon now. And every pothole meens buying a new 250 doller tier.