Multijunction (MJ) solar cells have the potential to operate across the entire solar spectrum, for ultrahigh efficiencies in solar energy harvesting. We present materials and strategies of using printed MJ solar cell structures to bypass the challenges in conventional multijunction cell design. Firstly, microscale, quadruple junction (InGaP/GaAs/InGaAsNSb//Ge), four-terminal solar cells are fabricated by printing-based assembly with a refractive index matched interface material As2Se3. We obtain solar cells with measured efficiencies of 43.9% at concentrations exceeding 1000 suns, and modules with efficiencies of 36.5%. Secondly, we present a printed MJ cell architecture with low refractive indices as interfaces, providing further enhanced capabilities in photon recycling and photon extraction. Experiments demonstrate that thin-film GaAs devices printed on low-index substrates exhibit improved photon recycling, leading to increased open-circuit voltages, consistent with theoretical predictions. These concepts represent important aspects of design for solar cells that approach thermodynamic efficiency limits for full spectrum operation.