Multiplexed volume Bragg gratings can be applied to many types of broad- and narrowband spectral systems. However, there are often deleterious side effects to combining several gratings into a single holographic optical element, including loss of efficiency in diffracted waves of interest and the introduction of spurious waves. Design of these spectral systems requires analysis methods that are flexible and efficient and that take these side effects into account. We present a matrix-based algorithm for determining diffraction efficiencies of significant coupled waves in these multiplexed grating Holographic optical elements (HOEs). Several carefully constructed experiments with spectrally multiplexed gratings in dichromated gelatin verify our conclusions.