The quick answer is - it depends.
I put a set of BFG 255/85R16 MT on my 2001. Had about 3/4-inch clear between the dual rear sidewalls. And, I was able to lower rear tire pressure as low as 30PSI without changing that clearance significantly. (Keep in mind, these 255's are a D-rated tire - 65PSI max. ) But, I didn't haul more than 500lbs or so with those, so I don't know how they would do with a load. Got the BFG tires replaced; had a bad set that couldn't be balanced; went back with stock size Michelins (235/85) because I couldn't find another 255 quickly.
However - is the 2004 model in your signature the dually you're asking for? If so, don't those 3rd-gen models have 17-inch wheels?
Hope this helps,
John