Holographic conformal field theories exhibit dramatic changes in the structure of their operator algebras in the limit where the number of local degrees of freedom (N) becomes infinite. An important example of such phenomena is the violation of the additivity property for algebras associated to local subregions. I will first review several examples of superadditive algebras in quantum field theory and then investigate their consequences in the context of holographic duality. As an important application, I will demonstrate how superadditivity of local algebras is intimately related to the ability of holographic field theories to perform quantum tasks that would naievely be impossible. Finally, I will argue that the connected wedge theorems (CWTs) of May, Penington, Sorce, and Yoshida, which characterize holographic protocols for quantum tasks, can be re-phrased in terms of superadditive algebras. This re-phrasing allows for a potential generalization of the CWTs into an equivalence statement.