Tandem solar cells involving metal-halide perovskite subcells offer routes to power conversion efficiencies (PCEs) that exceed the single-junction limit; however, reported PCE values for tandems have so far lain below their potential due to inefficient photon harvesting. Here we increase the optical path length in perovskite films by preserving smooth morphology while increasing thickness using a method we term boosted solvent extraction. Carrier collection in these films - as made - is limited by an insufficient electron diffusion length; however, we further find that adding a Lewis base reduces the trap density and enhances the electron-diffusion length to 2.3 µm, enabling a 19% PCE for 1.63 eV semi-transparent perovskite cells having an average near-infrared transmittance of 85%. The perovskite top cell combined with solution-processed colloidal quantum dot:organic hybrid bottom cell leads to a PCE of 24%; while coupling the perovskite cell with a silicon bottom cell yields a PCE of 28.2%.