Composite composites are entities that are important in physics and engineering and are a class of compounds actively investigated for their dielectric properties. Such systems consist of composite inclusions multicomponent materials embedded in a matrix of a distinct material. The effects of volume fraction, permittivity, shape and thickness of the various constituents on the complex permittivity, in the quasistatic approximation, of the heterostructures are reported. We use an ab initio numerical technique for the evaluation of the dielectric characteristics of composite composites, arranged in a regular simple cubic lattice, which is based on the field calculation package PHI3D and the resolution of boundary integral equations. This method is exact in the sense that all internal electric multipole interactions are taken into account. Typical results presented for spheres and ellipsoids indicate that any approach based solely on the dipole approximation must fail to predict the effective permittivity of dielectric heterostructures.