The successful implementation of an airborne propulsion system based on hydrogen-powered fuel cell technology highly depends on the development of an efficient, lightweight and compact air supply compressor. Meeting these requirements by designing the compressor using conventional single-point preliminary design methods can be challenging, due to the very wide range of corrected mass flow rate and pressure ratio values that the air supply compressor must be able to accommodate. The article presents a multi-point design methodology for the preliminary design of centrifugal compressors of air supply systems. The method is implemented in an in-house code, called TurboSim, and allows to perform single- and multi-objective constrained optimization of vaneless centrifugal compressors. Furthermore, an automatic design point selection method is also available. The accuracy of the compressor lumped-parameter model is validated against experimental data obtained on a high-pressure-ratio single-stage vaneless centrifugal compressor from the literature. Subsequently, the design methodology is applied to optimize the compressor of the air supply system of an actual fuel cell powertrain. The results, compared to those obtained with a more conventional single-point design method, show that the multi-point method provides compressor designs that feature superior performance and that better comply with the specified constraints at the target operating points.