It's notoriously difficult to find tires for the original Jeep Grand Cherokee SRT8. Staggered sizing and short sidewalls means very few choices, and none of those choices are intended for serious off-road use. And while most SRT8 owners don't plan to venture off the road, a Jeep is still a Jeep! There is always some temptation to head for adventure off the beaten path.
The newer Grand Cherokee SRT8, running 295/45R20 on all four corners, isn't much better for finding off-road tire options. However, the vehicle will fit the slightly larger 305/45R20 size. While it isn't a common size, it does provide Cherokee SRT8 owners the option to install the Yokohama Geolandar A/T-S.
Consistently ranked in the top ten in survey results in the On-/Off-Road All-Terrain performance category, the Geolandar A/T-S provides a nice mix of solid road handling with traction capability on loose surfaces. It's also designed to deliver long mileage and promote even wear while providing year-round traction, even in the snow.
If you want to let your SRT8 show its Jeep side, then take a look at the Yokohama Geolandar A/T-S.