You can stuff 31X10.5-15 tires into the wheel wells of the 2010-2011 but there is quite a bit of rubbing. Cranking the torsion bars will help some but the best way to fix the problem is to install torsion keys and axle block from a 2007 and earlier Ranger. The front will get about 1.5” of lift.
With those installed, the only rubbing you have is a little bit on the rubber splash shield on the passenger side and a small amount on the bends of the anti sway bar.
For your 16” rims, that would be 275/70R16 = 31.2X11-16
For a 32” tire, you could go with 265/75R16 = 31.7X10.5-16 if you do the pre-2008 lift. How much rubbing or lack there of
@Uncle Gump would have to answer.
Anything bigger is going to require a body lift, a suspension lift, or both.
EDIT: Part of the rubbing issue is a hump in the plastic splash guard of the front wheel well on the driver’s side. I don’t know if the earlier Rangers had that or not. So, something to consider when it comes to 32” tires and whether you can put up with it or not. It wouldn’t be a constant rub. Only when you hit bumps.
Also, I’m not a walking encyclopedia. I just happened to be doing research on the subject and swapping to 16” rims this morning. Thus, had the information written down and on hand.