We examine the potential of a multijunction spectrum-splitting photovoltaic (PV) solar energy system with perovskite PV cells. Spectrum splitting allows combinations of different energy band gap PV cells that are laterally separated and avoids the complications of fabricating tandem stack architectures. Volume holographic optical elements have been shown to be effective for the spectrum-splitting operation and can be incorporated into compact module packages. However, one of the remaining issues for spectrum splitting systems is the availability of low-cost wide band gap and intermediate band gap cells that are required for realizing high overall conversion efficiency. Perovskite PV cells have been fabricated with a wide range of band gap energies that potentially satisfy the requirements for multijunction spectrum-splitting systems. A spectrum-splitting system is evaluated for a combination of perovskite PV cells with energy band gaps of 2.30, 1.63, and 1.25 eV and with conversion efficiencies of 10.4%, 21.6%, and 20.4%, respectively, which have been demonstrated experimentally in the literature. First, the design of a cascaded volume holographic lens for spectral separation in three spectral bands is presented. Second, a rigorous coupled wave model is developed for computing the diffraction efficiency of a cascaded hologram. The model accounts for cross-coupling between higher diffraction orders in the upper and lower holograms, which previous models have not accounted for but is included here with the experimental verification. Lastly, the optical losses in the system are analyzed and the hypothetical power conversion efficiency is calculated to be 26.7%.