Convex operational models (COMs) are considered as great extrapolations to larger settings of any statistical theory. In this article, we generalize the maximum entropy principle (MaxEnt) of Jaynes' to any COM. After expressing MaxEnt in a geometrical and lattice theoretical setting, we are able to cast it for any COM. This scope-amplification opens the door to a new systematization of the principle and sheds light into its geometrical structure.Instituto de Física La PlataConsejo Nacional de Investigaciones Científicas y Técnicas