97 F350 PSD Biggest tire I can run!!??

[polarisrider4life]

I have a 97 f350 PSD all stock. the stock tires are 235/85/16. I'm sick of getting stuck in the mud with such skinny tires so what tire size can i go to get a more wide footprint making contact with the road? I dont want to modify the truck in any way, i just need to know what size i can get away with without hitting the inside of my wheel wells while turning and not scuffing the top of the wells when i hit a bump ya know?

[CT Performance, Inc.]

Space the bumper out 1" and if your springs haven't saged you should clear 35"