* Lift Kit: The most significant factor. A stock truck will have severe limitations. A lift kit (suspension lift and/or body lift) dramatically increases the space available for larger tires. The height of the lift kit directly impacts the maximum tire size.
* Wheel Backspacing: The distance between the mounting surface of the wheel and its inner edge. Incorrect backspacing can cause rubbing on the frame, suspension components, or body.
* Tire Size and Type: Even with a lift, extremely wide tires might rub. The overall diameter (height) is the most critical factor, but width also plays a role. Mud terrain tires tend to have a larger overall diameter than all-terrain or street tires of the same size designation.
* Fender Trimming: Some owners are willing to trim their fenders to accommodate larger tires. This is risky and can negatively impact the truck's structural integrity if not done properly.
Without a lift kit: You're likely limited to tires within a very small range of the stock tire size. Trying to fit much larger tires will result in rubbing and potential damage.
With a lift kit: With a significant lift (e.g., 6 inches or more), you could potentially fit tires in the 35-inch range or even slightly larger, *but this is highly dependent on the other factors above*. Some people even go bigger with extensive modifications.
Recommendation: Before purchasing larger tires, thoroughly research lift kits specifically designed for your 1997 F-250 Power Stroke 4x4. Consult forums and communities dedicated to these trucks (like Ford Truck Enthusiasts forums) to see what others have successfully done with similar trucks and lift kits. Measurements and careful planning are crucial to avoid problems. It's also best to consult a reputable tire shop and/or off-road specialist for advice.