Gas turbine engine generator switchable drive

A gas turbine engine (20) includes a first spool (40), a first gear system (72) connected to and driven by the first spool (40), a second spool (38), and a second gear system (70) connected to and driven by the second spool (38). A first starter-generator (60) has a first shaft (88) with a switchable coupling (74) connected to the first shaft (88). The switchable coupling (74) selectively couples the first starter-generator (60) to the first gear system (72) when the switchable coupling (74) is in a first position and selectively couples the first starter-generator (60) to the second gear system (70) when the switchable coupling (74) is in a second position. And a corresponding method for operating a gas turbine engine.