Research within density functional theory (DFT) has led to a large set of conceptual and computational methodologies to explore and understand the electronic structure of molecules and solids. Among the most commonly employed techniques in DFT are those of hybrid functionals, which are capable of producing accurate results for diverse properties, with notable exceptions. However, other techniques have been proposed to address limitations in the application of conventional hybrid functional techniques, especially to cases where a single reference is insufficient to achieve a proper description of the system of interest. In this paper we consider several previous developments in the field for the combination of local and nonlocal potentials and show that they can be formalized within the constrained-search Levy formalism, offering routes and ideas for the development of (nontraditional) density functionals, especially for treating strongly correlated regions of a molecule. The proposed formalism is centered around the idea of decomposing into domains the differential volume elements that are present in the definition of the electronic repulsion operator, which is contained in the electronic Hamiltonian, but this can also be applied to other operators as well. We show that the domain decomposition leads to a formulation that allows for the combination of different theories: DFT, correlated wave function theory, and Hartree-Fock, among others. This combination could accelerate the computation of electronic properties and allow for explicit inclusion, at the wave function level, of correlation effects, as in configuration-interaction theory. Our discussion covers both single- and multideterminantal methods. We demonstrate the approach through a simple application to the electronic structure of the methane and ethylene molecules, in which nonlocal exchange is applied to a given set of atoms, or domains, with the remaining atoms modeled with the local density approximation.