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 (413, 414) 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 (413, 414), wherein the tower shaft includes an outer gear enmeshed with the transmission gearing (413, 414), and the transmission gearing (413, 414) 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 (413, 414), wherein the first clutch includes a disengaged state whereby the transmission gearing (413, 414) is uncoupled from the tower shaft, and an engaged state whereby the transmission gearing (413, 414) is coupled to the tower shaft; and a second clutch between the transmission gearing (413, 414) and the second shaft, wherein the second clutch includes a disengaged state whereby the transmission gearing (413, 414) is uncoupled from the second shaft, and an engaged state whereby the transmission gearing (413, 414) 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 (413, 414) 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 (413, 414), wherein the tower shaft includes an outer gear enmeshed with the transmission gearing (413, 414), and the transmission gearing (413, 414) 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 (413, 414), wherein the first clutch includes a disengaged state whereby the transmission gearing (413, 414) is uncoupled from the tower shaft, and an engaged state whereby the transmission gearing (413, 414) is coupled to the tower shaft; and a second clutch between the transmission gearing (413, 414) and the second shaft, wherein the second clutch includes a disengaged state whereby the transmission gearing (413, 414) is uncoupled from the second shaft, and an engaged state whereby the transmission gearing (413, 414) is coupled to the second shaft.