Information theory provides a framework for answering fundamental questions about the optimal performance of many important quantum communication and computational tasks. In many cases, the optimal rates of these tasks can be expressed in terms of regularized formulas that consist of linear combinations of von Neumann entropies optimized over state extensions. However, evaluation of regularized formulas is often intractable, since it involves computing a formula’s value in the limit of infinitely many copies of a state. To find optimized linear entropic functions of quantum states whose regularized versions are tractable to compute, we search for examples which are additive. We use the method of cross2017uniform, which considers bipartite formulas, to identify convex polyhedral cones of tripartite correlation measures which satisfy a stronger a form of additivity called uniform additivity. We rely only on strong subadditivity of the von Neumann entropy and use these cones to prove that three previously established tripartite optimized correlation measures are additive.