A high-power nested Hall thruster was operated with cathode flow fractions from 7 to 3% of the total anode flow rate in a two-channel operating configuration at 27 kW total discharge power. The thruster was operated with a state-of-the-art high-current cathode featuring novel external propellant injectors. In stand-alone testing, the cathode has been shown to operate stably up to 300 A with a total flow rate of 36 sccm of xenon. The experiment reported here demonstrated the extensibility of these low flow rates to operation when integrated into the thruster. The impact of the lower-than-nominal flow rates was evaluated using direct thrust measurements, plasma diagnostics, and high-speed current measurement. These results were used to calculate the cathode coupling voltage, most probable beam ion voltage, anode efficiency, total efficiency, and the discharge current oscillation magnitude. It was found that the thruster could be operated with little identifiable change in behavior or performance with a cathode fraction as small as 4%. When the cathode flow fraction was reduced beyond that, the thruster exhibited reduced performance. Implications of these results for future high-power operation of Hall thrusters are discussed.