Photon upconversion via triplet-triplet annihilation (TTA-UC) provides a pathway to overcoming the thermodynamic efficiency limits in single-junction solar cells by allowing the harvesting of sub-bandgap photons. Here, we use mixed halide perovskite nanocrystals (CsPbX3, X = Br/I) as triplet sensitizers, with excitation transfer to 9,10-diphenylanthracene (DPA) and/or 9,10-bis[(triisopropylsilyl)ethynyl]anthracene (TIPS-An) which act as the triplet annihilators. We observe that the upconversion efficiency is five times higher with the combination of both annihilators in a composite system compared to the sum of the individual single-acceptor systems. Our work illustrates the importance of using a composite system of annihilators to enhance TTA upconversion, demonstrated in a perovskite-sensitized system, with promise for a range of potential applications in light-harvesting, biomedical imaging, biosensing, therapeutics, and photocatalysis.