A system for supplying a turbine engine with fluid includes a first low-pressure pump, a downstream hydraulic resistance and a high-pressure volumetric pump located between the first low-pressure pump and the downstream hydraulic resistance. The downstream hydraulic resistance includes at least one element selected among a fluid proportioning unit, a filter, a flow meter, an exchanger, a cut-off valve and an injection system. The supply system includes a second low-pressure pump and a supply variator configured such as to vary the flow of fluid supplied to the second low-pressure pump, the second low-pressure pump and the supply variator being located parallel to the first low-pressure pump.