A gas turbine engine comprising: a first spool comprising a first compressor and a first turbine mounted to a first shaft ; a second spool comprising a second compressor and a second turbine mounted to a second shaft ; a third spool comprising a third compressor , a third turbine , and a shaft gear mounted to a third shaft ; an accessory gearbox comprising: a housing ; and a transmission gearing ; a plurality of output shafts ; an accessory gearing rotationally coupled to the plurality of output shafts , wherein the transmission gearing and the accessory gearing are enclosed within the housing ; a plurality of engine accessories, each engine accessory of the plurality of engine accessories is rotationally coupled to one of the plurality of output shafts ; a tower shaft including an inner gear enmeshing with the shaft gear and extending radially outward from the third shaft to the transmission gearing , wherein the tower shaft includes an outer gear enmeshed with the transmission gearing , and the transmission gearing enmeshes with the accessory gearing and rotationally couples the tower shaft to the second shaft ; a first clutch between the tower shaft and the transmission gearing , wherein the first clutch includes a disengaged state whereby the transmission gearing is uncoupled from the tower shaft , and an engaged state whereby the transmission gearing is coupled to the tower shaft ; and a second clutch between the transmission gearing and the second shaft , wherein the second clutch includes a disengaged state whereby the transmission gearing is uncoupled from the second shaft , and an engaged state whereby the transmission gearing is coupled to the second shaft . a first spool comprising a first compressor and a first turbine mounted to a first shaft ; a second spool comprising a second compressor and a second turbine mounted to a second shaft ; a third spool comprising a third compressor , a third turbine , and a shaft gear mounted to a third shaft ; an accessory gearbox comprising: a housing ; and a transmission gearing ; a housing ; and a transmission gearing ; a plurality of output shafts ; an accessory gearing rotationally coupled to the plurality of output shafts , wherein the transmission gearing and the accessory gearing are enclosed within the housing ; a plurality of engine accessories, each engine accessory of the plurality of engine accessories is rotationally coupled to one of the plurality of output shafts ; a tower shaft including an inner gear enmeshing with the shaft gear and extending radially outward from the third shaft to the transmission gearing , wherein the tower shaft includes an outer gear enmeshed with the transmission gearing , and the transmission gearing enmeshes with the accessory gearing and rotationally couples the tower shaft to the second shaft ; a first clutch between the tower shaft and the transmission gearing , wherein the first clutch includes a disengaged state whereby the transmission gearing is uncoupled from the tower shaft , and an engaged state whereby the transmission gearing is coupled to the tower shaft ; and a second clutch between the transmission gearing and the second shaft , wherein the second clutch includes a disengaged state whereby the transmission gearing is uncoupled from the second shaft , and an engaged state whereby the transmission gearing is coupled to the second shaft . <EOS>