We report on the progress in developing lattice-matched GaAs-based solar cells with focus on developing AlGaInP, AlGaAs, and GaInNAsSb materials, aiming at achieving a wide spectral coverage, that is, 0.7-2.2 eV. To this end, we first benchmark the performance of an upright four-junction GaInP/GaAs/GaInNAsSb/GaInNAsSb solar cells grown by molecular beam epitaxy on p-GaAs substrates with bandgaps of 1.88, 1.42, 1.17, and 0.93 eV, respectively. The four-junction cell exhibited an efficiency of 39% at 560-sun illumination while showing good electrical performance even up to 1000 suns. As a first step to further improve the efficiency toward 50% level, we demonstrate AlGaInP (>2 eV) and GaInNAsSb (<0.8 eV) subcells. We prove that AlGaInP cells with 0.1 Al composition would exhibit current-matching condition when being incorporated in a five-junction architecture together with two GaInNAsSb bottom and AlGaAs top junctions. Furthermore, current matching required for a six-junction tandem architecture is achieved for an Al composition of 0.26. Overall, the results open a practical path toward fabrication of lattice-matched solar cells with more than four junctions.