Hybrid DFT methods, where the functional is supplemented with Hartree-Fock exchange, have become increasingly popular due to their low cost and decent accuracy. Double hybrids, which mix in an MP2 contribution, have also been developed as a way to improve the accuracy.
Has this idea been extended to other Post-SCF methods? For example, one could consider doing coupled cluster or configuration interaction calculations where a DFT wavefunction is used as the primary configuration. If not, is there a major hurdle, technical or theoretical, that prevents this from being done?