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Recent advances in photonic optimization have enabled calculation of performance bounds for a wide range of electromagnetic objectives, albeit restricted to single-material systems. Motivated by growing theoretical interest and fabrication advances, we present a framework to bound the performance of photonic heterostructures and apply it to investigate maximum absorption characteristics of multilayer films and compact, free-form multi-material scatterers. Limits predict trends seen in topology-optimized geometries – often coming within factors of two of specific designs – and may be utilized in conjunction with inverse designs to predict when heterostructures are expected to outperform their optimal single-material counterparts.