The biggest tire you can run on a 4 inch lift is a 32. People have stuffed 33’s on before, but with no room left for articulation or tight steering, which is very important off-road. They also had to do a lot of cutting, which should be avoided. Wheel spacers make matters worse. 32’s are plenty large for the KK, and I run 31’s in mine with the JBA 4” lift and they’ve been more than enough for the power line cuts, bulldozed firebreaks, and unimproved forest roads that I drive on for my work. Plus the highway manners and handling are much better than stock due to the JBA springs.
One other consideration is that if you get above 31’s you’ll need to regear your differentials to keep the engine from lugging and the transmission from being constantly stressed out. I would like to go from the stock 3.73 gears to 4.10’s with my 31’s but in the meantime the loss of power and mpg is livable. It would not be happy if you tried 32’s on stock gearing. You’ll need to plan on going to 4.56 or 4.88 with 32’s (and certainly 4.88 with 33’s). Stock is 3.73 gears.
Here is what 31’s look like with the 4” lift.
