Systems are provided for a limited slip differential (LSD). The LSD comprises a two-piece differential case, an intermediate floating piece positioned in an interior of the two-piece differential case and configured to slide axially therein. The LSD, further comprises a first side gear and a second side gear meshed with gears of the intermediate floating piece, a first disc spring mounted on the first side gear and a second disc spring mounted on the second side gear, a first clutch pack mounted on the first side gear and positioned between the first disc spring and a lip of the first side gear, and a second clutch pack mounted on the second side gear and positioned between the second disc spring and a lip of the second side gear, and a shim mounted on the second side gear and positioned axially between the second disc spring and the two-piece differential case.