A turbine engine fuel supply system includes a priority flow line, a plurality of secondary fuel loads, a fluid-powered metering pump, a mechanically-driven fuel pump, and an electric machine. The fluid-powered metering pump, upon receiving fuel at its fuel inlet, rotates at a rotational speed, discharges the fuel from its fuel outlet at a flow rate dependent on the rotational speed, and supplies a first drive torque. The mechanically-driven fuel pump receives a second drive torque and, in response, draws fuel into its fuel inlet and discharges the fuel from its outlet to the fluid-powered metering pump fuel inlet to drive the fluid-powered metering fuel pump. The electric machine receives the first drive torque from the fluid-powered metering pump and generates electrical power.