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my 2006 King ranch came with 20" wheels and it has 285 65 R 20 wich is 34.6" tall and there is no clearance issues with them. The 20" wheels are an option on the King Ranch. I think if you stay with a 285 series tire you can easily go to 34" with out a problem. They are just hard to find. You will run into problems with the wide tires.
I agree on the 285 75 16, it's what I have for a couple weeks more yet, and I used to say they didn't rub, but apparently, on occasion, I'm contacting the plastic inside the fender.
I also think *operative word* that the older body style like mine - 01 - has a little less room than the newer.
my 2006 King ranch came with 20" wheels and it has 285 65 R 20 wich is 34.6" tall and there is no clearance issues with them. The 20" wheels are an option on the King Ranch. I think if you stay with a 285 series tire you can easily go to 34" with out a problem. They are just hard to find. You will run into problems with the wide tires.
you also have a different suspension up front, the pre 05's have less clearance up front
Correct the new suspension is a coil. On my 1999 SD I ran 315 75 R16 (35)on it stock for a few weeks while my leveling kit was shipping to me. They did have clearance problems. The issue is not in height as much as it is width Les Schwab sells a 255 85 R16 which is over 33" tall. I know someone who runs those and chains on all four tires durring the winter on a stock 2000 with the 7.3 diesel. I think you can run a 35" as long as the section width is under the 285mm.