Two-dimensional dipolar mixtures consisting of spherical particles with unequal susceptibilities are shown to order to an enormous variety of crystalline structures, whose geometry can be tuned by the stoichiometry of the compound, the susceptibility ratio, as well as the density. Our results are based on the application of genetic algorithms, which allow for an efficient and unbiased search over the parameter space. Structures that are practically degenerate energetically are discovered at various parameter combinations. Implications on the ability to tune the phononic spectra of such composite materials are discussed.