A gas turbine engine comprising: a support structure ; a plural spool assembly supported for rotation about an axis by the support structure , the plural spool assembly including a first spool and a second spool ; an accessory supported by the support structure , the accessory configured to change between a motor mode and a generator mode; and a transmission configured to transmit mechanical power between the accessory and at least one of the first spool and the second spool , the transmission including a first transmission arrangement and a second transmission arrangement ; the first transmission arrangement of the transmission operably coupling the first spool and the accessory and, when the accessory is in the generator mode, configured to transmit mechanical power from the first spool to the accessory for generating electric power at the accessory ; the second transmission arrangement of the transmission operably coupling the second spool and the accessory and, when the accessory is in the motor mode, configured to transmit mechanical power from the accessory to the second spool , wherein the first transmission arrangement comprises a first gear train from the first spool to the accessory and wherein the second transmission arrangement comprises the first gear train and a second gear train arranged in-series from the accessory to the second spool , wherein the first gear train terminates at a first end gear that is rotationally fixed to the first spool , the second gear train branching from the first gear train to operably connect to the second spool , wherein the second gear train terminates at a second end gear that is rotationally fixed to the second spool and at a third end gear that branches from the first end gear; and wherein the first gear train has a fixed train arrangement such that the first spool and the accessory remain coupled for mechanical power transmission both when the accessory is in the generator mode and is in the motor mode. a support structure ; a plural spool assembly supported for rotation about an axis by the support structure , the plural spool assembly including a first spool and a second spool ; an accessory supported by the support structure , the accessory configured to change between a motor mode and a generator mode; and a transmission configured to transmit mechanical power between the accessory and at least one of the first spool and the second spool , the transmission including a first transmission arrangement and a second transmission arrangement ; the first transmission arrangement of the transmission operably coupling the first spool and the accessory and, when the accessory is in the generator mode, configured to transmit mechanical power from the first spool to the accessory for generating electric power at the accessory ; the second transmission arrangement of the transmission operably coupling the second spool and the accessory and, when the accessory is in the motor mode, configured to transmit mechanical power from the accessory to the second spool , wherein the first transmission arrangement comprises a first gear train from the first spool to the accessory and wherein the second transmission arrangement comprises the first gear train and a second gear train arranged in-series from the accessory to the second spool , wherein the first gear train terminates at a first end gear that is rotationally fixed to the first spool , the second gear train branching from the first gear train to operably connect to the second spool , wherein the second gear train terminates at a second end gear that is rotationally fixed to the second spool and at a third end gear that branches from the first end gear; and wherein the first gear train has a fixed train arrangement such that the first spool and the accessory remain coupled for mechanical power transmission both when the accessory is in the generator mode and is in the motor mode. <EOS>