My answer.... You can go up about 1 size on the middle number (e.g., 215 55 16 TO 215 60 16), but not much.
If you go too high in tire size, the tires will rub and make noise against the suspension when you go over bumps or turn the steering on turns....
You will get more distance per rotation of the tire, but it will not be a big difference....
The best reason to do this is when the stock tires are very sensitive to any bumps or cracks in the road because the are low profile (e.g, not much distance between the road and the rim, like 45, 50, 55s (second number). I have improved the ride by going up one size of the middle number.
PS - Tire places do not like to sell you a different size tire than what their book says...