Pirelli's Scorpion 2.4" LITE range might be just the tyres that your down-country bike needs.
On the dirt
As when I tested the 2.2" Scorpions, my go to was the Rear specific in the back with the Mixed on the front. Pirelli state that this is the most versatile option, mixing excellent traction with good rolling speed. While this time I was on larger tyres with a seriously strong rear tyre, I can only agree with Pirelli.
I did spend some time getting pressures just right, and even dropped below 20psi in the back to 19.5, with 19psi in the front. I was testing this on my Norco Revolver FS with a 120mm fork and 100mm of rear travel. While the frame is rated to 2.35" tyres, the 2.4" fit fine.
I took this combination over about 300km of mixed terrain. From loose and crumbly moto trails in places I shouldn't have been, to purpose made singletrack in the local bike parks, and everything inbetween. The braking and climbing traction afforded by the Rear specific tyre was really impressive, and the stability when getting out of shape in ruts was an advantage over the thinner casing tyres I often run. But when one particular ride had me needing to go a very, very long way around to avoid trespassing and testing whether posted threats of violence would be adhered to or not - the heavy Rear specific tyre did make itself known. If you're the kind of rider who rides to the trails a lot and does a lot of climbing and distance, then the Rear specific tyre might just be too much.
So - I fitted the Hard conditions on the back, dropping a chunk of weight, getting some faster rolling speed and also dialling up the compliance thanks to the 120tpi casing. I did have to bump to 20.5psi, which is still pretty low all things considered.
The thing is, I noticed very little change in traction - save for hard braking and really loose climbs. Both of these were more on the extreme end of what you might experience in most trail networks, as it was when trying out new lines on a map well over the range behind my place. So steep descents well over 20%, and similar climbs back up.
It's worth remembering that Pirelli don't say that the Rear specific tyre has to be used. Instead, it's just what they have designed to be for optimum performance on the back for durability, braking and accelerating.