A transmission includes an input shaft, an output shaft, at least five planetary gearsets, a variable-ratio unit, and at least five clutches. The at least five clutches are selectively engageable in combination with one another to select one of a plurality of operating modes including at least one reverse mode, at least five forward modes, and at least five transition modes. One of the at least five transition modes is configured to transition the transmission from the at least one reverse mode to one of the at least five forward modes. Another one of the at least five transition modes is configured to transition the transmission from the one of the at least five forward modes to another of the at least five forward modes. Each of the at least five transition modes includes a fixed speed ratio defined between the input shaft and the output shaft.