We replace the traditional grating used in a dispersive spectrometer with a multiplex holographic grating to increase the spectral range sensed by the instrument. The multiplexed grating allows us to measure three different, overlapping spectral bands on a color digital focal plane. The detector's broadband color filters, along with a computational inversion algorithm, let us disambiguate measurements made from the three bands. The overlapping spectral bands allow us to measure a greater spectral bandwidth than a traditional spectrometer with the same sized detector. Additionally, our spectrometer uses a static coded aperture mask in the place of a slit. The aperture mask allows increased light throughput, offsetting the photon loss at the broadband filters. We present our proof-of-concept dispersion multiplexing spectrometer design with experimental measurements to verify its operation.