Mechanically stacked, tandem thermophotovoltaic (TPV) cells featuring integrated air-bridge InGaAs and InGaAsP subcells achieve high spectral efficiency and emission temperature versatility. Thermocompression bonding of electrodes on opposing single air-bridge cells increases out-of-band reflectance (R OUT ) compared to cells lacking air bridges. We report a 0.74/0.74 eV homotandem exhibiting R OUT = 96.4%. When operated in a multiterminal arrangement, the homotandem achieves 38% efficiency, marking a 20% absolute improvement over a comparable two-terminal configuration. We also demonstrate a 0.9/0.74 eV heterotandem with R OUT = 97.2% and spectral efficiency approaching 80%. By minimizing losses associated with parasitic absorption and current mismatch, the tandem substantially expands the emission temperature range while preserving high efficiency. This leads to a reduction in the cost of energy storage by over 40%. The air-bridge tandem technology paves the way for high-performance tandem cells compatible with a variety of heat sources unrestricted by the choice of subcell materials.