A multi-mode transmission is configured to transfer torque among an internal combustion engine, torque machines and an output member. A method for controlling shifting in the transmission includes, in response to a command to execute a range shift in the transmission to a target transmission range: applying mechanical braking torque to reduce output torque from the transmission to off-load torque from an off-going clutch, operating in a pseudo-gear range to synchronize an oncoming clutch, and applying the oncoming clutch to establish the transmission in the target range.