Missmy06

I have Goodyear Wrangler Duratracs on mine and they seem to do everything well and are very quiet considering how aggressive the tread is. I have 25k miles on mine and they still have a lot of life left. I am very happy with them.

Brad-150

Another vote for BFG KO2's here.

Also, if your truck is a 4x4, even at stock height, you can go larger than 31 inches if you want. I'm not sure about 2x4

jdunk54nl

Not highway speeds, but my ridge grapplers did fine in 12-18" of off road snow. Max speed was about 45mph and I wasn't at all concerned with the 1000ft drop off of a cliff a foot or so away from me.
I also liked the K02's I had on my last truck. They never let me down, but I do like the ridge grapplers better than the K02's.

RLXXI

Stock 4x4 tires are 32" from the factory. at least with 18" wheels any way. Dunno about other wheel sizes. 4x2 are 30" in 18" wheels.
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Brad-150

Exactly. OP said he thought 31" was the biggest he could fit, but he hasn't said what configuration his truck is.