Don't go wider than 11.5" if stock wheels, and you shouldn't have to worry about clearance when off-road.
I and a couple others run 33x10.5R15's with no problem, essentially stock trucks.
They are a bit narrow, BUT they are still wider than the 235/75R15's, and just as wide as the 31's, just taller. So from the rear they don't look any different than the 31's, but on the side they fill the wheelwells out like any other 33. Plus the narrower tires are better in water on pavement, and snow/mud you can get to the bottom of. Better economy as well, and my BFG A/T's so far are wearing very well.
An A/T tire is a compromise, but they make MT's in this size as well.