We control surface recombination in the mixed-cation, mixed-halide perovskite, FA(0.83)Cs(0.17)Pb(I0.85Br0.15)(3), by passivating nonradiative defects with the polymerizable Lewis base (3-aminopropyl)trimethoxysilane (APTMS). We demonstrate average minority carrier lifetimes >4 mu s, nearly single exponential monomolecular photoluminescence decays, and high external photoluminescence quantum efficiencies (>20%, corresponding to similar to 97% of the maximum theoretical quasi-Fermi-level splitting) at low excitation fluence. We confirm both the composition and valence band edge position of the FA(0.83)Cs(0.17)Pb(I0.85Br0.15)(3) perovskite using multi-institutional, cross-validated, X-ray photoelectron spectroscopy and UV photoelectron spectroscopy measurements. We extend the APTMS surface passivation to higher bandgap double-cation (FA and Cs) compositions (1.7, 1.75, and 1.8 eV) as well as the widely used triple-cation (FA, MA, and Cs) composition. Finally, we demonstrate that the average surface recombination velocity decreases from similar to 1000 to similar to 10 cm/s post APTMS passivation for FA(0.83)Cs(0.17)Pb(I0.85Br0.15)(3). Our results demonstrate that surface-mediated recombination is the primary nonradiative loss pathway in many methylammonium (MA)-free mixed-cation mixed-halide films with a range of different bandgaps, which is a problem observed for a wide range of perovskite active layers and reactive electrical contacts. Our study also provides insights to develop passivating molecules that help reduce surface recombination in MA-free mixed-cation mixed-halide films and indicates that surface passivation and contact engineering will enable near-theoretical device efficiencies with these materials.