Flexible perovskite solar cells (PSCs) hold great promise for the low-cost roll-to-roll production of lightweight single- and multijunction photovoltaic devices. Among the different deposition methods used for the perovskite absorber, the two-step hybrid vacuum-solution approach enables precise control over the thickness and morphology of PbI2. However, efficient conversion to perovskite is limited by diffusion of the organic cations in the compact lead halide layer. Herein, a multistage absorber deposition is developed by thermal evaporation of PbI2 and spin coating of CH3NH3I (MAI). The process relies on the different types of growth of vacuum-deposited PbI2 onto amorphous and crystalline surfaces. This approach represents a way to effectively increase the absorber thickness while tackling the limited MAI diffusion in the compact PbI2 film via a two-step deposition method. The efficiency of flexible PSCs is improved from 14.2 to 15.8% with multistage deposition. Furthermore, the use of an amorphous transparent conductive oxide (TCO), InZnO, enhances the mechanical resistance against bending with respect to conventional crystalline TCO-based flexible devices. Near-infrared transparent flexible PSCs are developed with an efficiency of 14.0% and average transmittance of similar to 74% between 800 and 1000 nm. Flexible perovskite/CIGS thin-film tandem devices are demonstrated with an efficiency of 19.6% measured in the four-terminal configuration.