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Stock height or lifted? OEM or aftermarket wheels?
OEM wheels are 16x7" with a +6mm offset.
I have Ultra Type 164 wheels that are 16x8" with a -6mm offset (basically an extra 1/2" on each side). I have 285/75-16 BFG AT KO2 tires and can go full lock in either direction without rubbing...but not by much.
I might be able to clear a little larger without rubbing the springs but anything larger (with full tread depth) would most likely rub on the fender liner.
There's no way I could fit 315/85-16 tires on my truck without rubbing with the wheels I have. That tire is 4" taller and more than 1" wider than what I have.
Once you venture into aftermarket wheels/spacers then that opens up more options for tire size even at stock height.
I have an '01 f350 (6.8) and 285/75-16 Mickey thompson ATZp3 on the stock wheels. I can make them touch the leaves if I crank it hard enough. I wouldn't want to go any bigger. I used to have the same basic truck, with the same wheels and 285 firestone A/Ts and it didn't rub at all, but they were much less aggressive tires. Point being, I wouldn't go wider than 285 unless you have the proper backspacing to make it work. As far as height, I believe my front leaves are a little tired and saggy, but with the way mine sits I don't think I'd want to go much taller either.