A gas turbine engine (10) has a LP spool (20) including an LP shaft (23) and a HP spool (40) including an HP shaft (43), an accessory gear box (AGB) (50) drivingly engaged to a plurality of accessories, an engine starter (52B) drivingly engaged to the AGB (50), and a drive shaft (30) drivingly engaged to the AGB (50). In a first engine mode, the drive shaft (30) is drivingly engaged to the HP shaft (43) and is disengaged from the LP shaft (23), the engine starter (52B) is in driving engagement with the HP shaft (43) via the drive shaft (30), and the LP shaft (23) is disengaged from the AGB (50). In a second engine mode, the drive shaft (30) is drivingly engaged to the LP shaft (23) and is disengaged from the HP shaft (43), the LP shaft (23) is in driving engagement with the AGB (50) via the drive shaft (30), and the HP shaft (43) is disengaged from the AGB (50).