As multi-material additive manufacturing technologies mature, a new opportunity for materials science and engineering emerges between the scale of the microstructure and the scale of an engineering component. Here we explore the problem of "mesostructure optimization," the computational identification of preferred point-to-point distributions of material structure and properties. We illustrate the opportunity with two simple example problems for 1D and 2D mesostructure optimization, respectively, namely (1) a functionally graded cylinder that is computationally optimized to redistribute the Hertzian contact stress fields and (2) a thin plate made of digital materials computationally designed to simultaneously maximize bending resistance and minimize total weight. The mechanical performance of materials in these two problems is significantly improved as compared to any monolithic-material counterpart, including a topology-optimized monolith in case (2). These results point to new opportunities for multi-objective performance enhancement in materials.