The new technique of sub-quarterwave multilayers is applied to design multilayers with more than two materials, with enhanced reflectance at 13.4 and 11.3 nm, the wavelengths of interest for the extreme ultraviolet lithography. We provide the spectrum of materials and the rules for material selection in order to design the multilayers with the highest possible reflectance. The paper addresses the highest limit of reflectance enhancement that can be theoretically attained with multi-material multilayer designs assuming ideal multilayers. The minimum polygon enclosing the complex refractive index of all available materials at 11.3 and 13.4 nm was constructed, and the reflectance of multilayers with combinations of materials from this polygon is shown. The technique of material selection was also used in the search of capping layers. Calculations with ideal multi-material multilayers applied to a nine-mirror optical system gave a significant throughput enhancement at the target wavelength, with a bandwidth that did not necessarily decrease when increasing the number of materials. The increased throughput was obtained for a wide range of angles of incidence.