I have a shortbed with a 31" spare.
Laterally, without measuring it appears there is BARELY enough space for 2 more inches on each side -- but if the axle shifts laterally when flexing the springs are going to rub the tire.
The 31 takes up ALL the space in the stock spare location. Behind the tire there is only about 1/4" of clearance, and the radius of the sheet metal pan seems to be about 31.5" so even if you moved the spare forward, it would be an awkward fit.
And moving it forward isn't much of an option because there's only about 2 to 3 inches in fron of the spare to the diff.
All in all, I'd say for a shortbed a 31x10.50 is about the limit. You might squeeze a 32 in there, but there's no way a 35 is going to work. A longbed might be slightly better.