A concept for the design of single-stack multilayer mirrors with multiple reflection peaks is presented. Its realization in the infrared is demonstrated by the sputter deposition of TiO2/Al2O3 bilayers on sapphire and HastelloyX substrates and corresponding reflection measurements. Even or odd higher-order interference peaks are selected by adjusting the optical thicknesses of the individual layers. The peak positions are very well reproduced by multiple scattering calculations. With the HastelloyX substrate, a potential application for high temperatures and aggressive atmospheres, e.g., in aircraft turbines, is addressed. A design for matching up to three turbine gas emission bands (CO2, H2O) is proposed.