A generalization of the single reference Coupled Cluster parameterization for the ground state wave function is proposed that includes substitution operators that annihilate the reference determinant, but which act nontrivially on the correlated part of the wave function. It is shown that an inclusion of such two-body operators can mimic the effect of conventional connected triple and higher excitation operators. Results obtained with Brueckner based Generalized Coupled Cluster Doubles theory (BGCCD-version x) are found to be comparable in accuracy to CCSD(T) and CCSDT for a number of difficult test cases. In the current version of the BGCCD approach we obtain correlated ionization potentials and electron affinities as a by-product of a ground state calculation. This multistate nature of the BGCCD-X approach can give rise to problems with intruder states similar as in Fock Space Coupled Cluster theory.