A transmission assembly for a machine is disclosed. The transmission assembly may have a clutch pack, a first pressure chamber, and a second pressure chamber. The transmission assembly may also have a first piston configured to push against the clutch pack when pressurized fluid is directed into the first pressure chamber, and a second piston configured to push against the first piston when pressurized fluid is directed into the first pressure chamber and inhibited from pushing against the first piston when pressurized fluid is directed into the second pressure chamber.