The rising number of proposed nanosatellite missions with Commercial Off-The-Shelf electronics to higher orbits necessitates innovative, compact, and lightweight radiation shielding. In this study, several thousand multilayer radiation shielding configurations were simulated against trapped particle spectra predicted for a geostationary transfer orbit to demonstrate how material combinations and layer structures can be selected to minimise the total ionising dose inside nanosatellites with constrained mass budgets. The Geant4 Radiation Analysis for Space (GRAS) application was used to calculate ionising dose deposition behind multilayer shielding. Thousands of planar shielding stacks were procedurally generated and simulated on top of silicon plates representing sensitive semiconductor devices. To allow for comparison between configurations, all shielding stacks had a total mass of 1.5 g/cm2, and shielding performance was evaluated based on the total ionising dose absorbed by the silicon plates. The simulations consistently show that configurations with low-atomic-number (low-Z) materials on top of high-Z materials yield the lowest doses. The two- and three-layer mass allocation optimisations demonstrate the non-linear dependence of ionising dose on mass allocation between materials. Optimised polyethylene-lead shields achieved up to 30% lower ionising doses compared to an equal mass of either of the two materials or up to 50% lower than the same mass of aluminium. Contrary to previous claims about Z-graded shielding, no significant improvements were observed for using more than two different materials, and optimisation of multilayer shields tends to reduce them to two-layer structures. Optimal multilayer radiation shielding depends on various factors and must be tailored to specific radiation environments and mission requirements. The primary contributions of this article are the methods presented for achieving this tailoring using open-source software and parallel computing. The multilayer simulations performed for this work resulted in an extensive dataset for multilayer shielding performance that enabled novel visualisations of the ionising dose dependence on shielding composition based on quantitative results.