Ive got a 33x10.5r15 in the back of mine.
I had to move the floor mounting points (welded a washer to the legs) to get it to clear either the tailgate or the rear seat, can't remember which. I don't believe tire width will be an issue, but anything more than 33" diameter and I'm pretty sure you'd hit the seat and/or the tailgate no matter what. There is VERY little clearance left in mine.