A transmission includes an input shaft, an output shaft, a variable-ratio unit, and a plurality of torque transmitting mechanisms. The plurality of torque transmitting mechanisms include a first clutch, a second clutch, a third clutch, and a fourth clutch. The transmission is operable to (i) engage the first clutch and the second clutch in a first operating mode and (ii) engage the first clutch and the third clutch in a second operating mode. The transmission is further operable to (i) engage the fourth clutch and disengage the second clutch during a first period of time and (ii) engage the third clutch and disengage the fourth clutch during a second period of time following the first period of time to transition from the first operating mode to the second operating mode.