Perovskite semiconductors hold a unique promise in developing multijunction solar cells with high-efficiency and low-cost. Besides design constraints to reduce optical and electrical losses, integrating several very different perovskite absorber layers in a multijunction cell imposes a great processing challenge. Here, we report a versatile two-step solution process for high-quality 1.73 eV wide-, 1.57 eV mid-, and 1.23 eV narrow-bandgap perovskite films. Based on the development of robust and low-resistivity interconnecting layers, we achieve power conversion efficiencies of above 19% for monolithic all-perovskite tandem solar cells with limited loss of potential energy and fill factor. In a combination of 1.73 eV, 1.57 eV, and 1.23 eV perovskite sub-cells, we further demonstrate a power conversion efficiency of 16.8% for monolithic all-perovskite triple-junction solar cells.