>>1130418>>1130432CC can take 2.0s with enough clearance to be safe depending on the tire, but with the wheel slammed that far back in the dropouts, indexed shifting is usually garbage.
Given however that the owner installed 2.0s on 19mm road rims and didn't even bother to install a cable stop for his rear brake I'm guessing they don't mind.
Honestly OP, I posted that Rock Lobster CC as a half-joke. You don't need 2.0s to take a Cross Check on single track, I'd even argue any trails that require a tire that big would also be a lot more fun on a frame with proper MTB geometry. I managed many summers with a 40-45c knobs riding the various cross-country trails here in WA and I am by no means an especially gifted rider (pic related)