Multilayer coatings with three layers were designed to yield an increase in normal-incidence reflectance in the extreme ultraviolet over that of the available single-layer coatings. Multilayer coatings based on Al, MgF(2), and either SiC or B(4)C were demonstrated to have higher reflectance than single layers of SiC and B(4)C in the spectral region from 57.9 nm to the H Lyman-alpha line (121.6 nm) and above. The increase in reflectance was higher at wavelengths close to 121.6 nm. Reflectance degraded slightly over time in the same way as for single layers. After a few months, multilayer coatings maintained higher reflectance than their single-layer counterparts.