An exemplary gas turbine engine assembly includes a first spool having a first turbine operatively mounted to a first turbine shaft, and a second spool having a second turbine operatively mounted to a second turbine shaft. The first and second turbines are mounted for rotation about a common rotational axis within an engine static structure. The first and second turbine shafts are coaxial with one another. First and second towershafts are respectively coupled to the first and second turbine shafts. An accessory drive gearbox has a set of gears. A compressor is driven by the first towershaft. The engine assembly further includes a starter generator assembly, and a transmission coupling the starter generator assembly to the first set of gears. The transmission is transitionable between a first mode where the starter generator assembly is driven at a first speed relative to the second towershaft, and a second mode where the starter generator assembly is driven at a different, second speed relative to the second towershaft.