The Kohn-Sham equations with constrained electron density (KSCED) embedding formalism of Wesoowski and coworkers was originally developed and is good for the case of two weakly interacting molecular regions with weakly overlapping densities, such as might be expected in describing solvation. A generalization is given here for the case of three molecular regions with strongly overlapping densities with the idea that this generalized theory can offer a better description of embedding in the context of situations that might be encountered in, for example, chemisorption on surfaces or active sites in enzymes. This three-partition generalization includes the original two-partition formalism as a special case. Time-dependent response theory equations are then developed for the two- and three-partition theories for application to the problem of the calculation of polarizabilities and other response properties, including excitation spectra, of embedded molecules or molecular structures.