Check out the Tech Tips here:
https://www.stovebolt.com/techtips/wheels/While we wait for the experts to chime-in, I looked at my dealer's handbook.
Please excuse my lack of knowledge but a stakebed is a flatbed with removable sides?
So what you have is the 3809?
According to the book, rear 17" wheels are standard and 18" duals are the option 295 but require the aux. spring option 267.
My take is that GM didn't design that model truck for taller sizes.
Maybe taller tires would rub holes it the bed bottom?
Also taller tires will require an adapter to make your speedometer read correctly.
