An accessory system for a gas turbine engine having a driveshaft with an axis of rotation is provided. The system includes a towershaft coupled to the driveshaft and rotatable about a towershaft axis of rotation. The towershaft includes a towershaft bevel gear. The system includes a primary shaft including a first bevel gear and a second bevel gear that each revolve about a primary shaft axis of rotation. The first bevel gear is coupled to the towershaft bevel gear. The system includes a secondary shaft including a third bevel gear and a fourth bevel gear that each revolve about a secondary shaft axis of rotation. The third bevel gear is coupled to the second bevel gear. The system includes a tertiary shaft including a fifth bevel gear that revolves about a tertiary shaft axis of rotation. The fifth bevel gear is coupled to the fourth bevel gear.