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. ??Specifically, I will demonstrate how the superadditive property is ??intimately related to the success of quantum error correcting code ??models of holography and then I will argue that the connected wedge ??theorems (CWTs) of May, Penington, Sorce, and Yoshida can be ??re-phrased in terms of superadditive algebras. This re-phrasing ?allows ??for the definition of a generalized scattering region for ?which a ??generalization of the CWTs can be formulated such that both ?the ??theorem and its converse should hold.