I have 26 x 2" Marathon Mondials on my 2016 Surly DT and there's still plenty of clearance. The bike could take a much wider tire, but I've got the widest finders that will fit in the frame and these 2" tires pretty much fill the fender out. So if the OP went lager than a 2" tire, things could get messy in the wet.

I've ridden from Bend, OR, out to the coast down to SF, up over Yosemite, Mono Lake, down the Owens Valley, across Death Valley, Las Vegas, Lake Mead, up into UT and down to the Grand Canyon with this set up. Some of that was on gravel. And although I wouldn't say it was Cadillac comfortable, I always felt safe and sure-footed; never like the bike was out of its element.