Electron and charge transfers are part of many vital processes in nature and technology. Ab initio descriptions of these processes provide useful insights that can be utilized for applications. A combination of the embedded cluster material model and nonorthogonal configuration interaction (NOCI), in which the cluster wave functions are expanded in many-electron basis functions (MEBFs) consisting of spin-adapted, antisymmetrized products of multiconfigurational wave functions of fragments (which are usually molecules) in the cluster, appears to provide a compromise between accuracy and calculation time. Additional advantages of this NOCI-Fragments approach are the chemically convenient interpretation of the wave function in terms of molecular states, and the direct accessibility of electronic coupling between diabatic states to describe energy and electron transfer processes. Bottlenecks in this method are the large number of two-electron integrals that have to be handled for the calculation of an electronic coupling matrix element and the enormous number of matrix elements over determinant pairs that have to be evaluated for the calculation of one matrix element between the MEBFs. We show here how we created a reduced common molecular orbital basis that is utilized to significantly reduce the number of two-electron integrals that need to be handled. The results obtained with this basis do not show any loss of accuracy in relevant quantities like electronic couplings and vertical excitation energies. We also show a significant reduction in computation time without loss in accuracy when matrix elements over determinant pairs with small weights are neglected in the NOCI. These improvements in the methodology render NOCI-Fragments to be also applicable to treat clusters of larger molecular systems with larger atomic basis sets and larger active spaces, as the computation time becomes dependent on the number of occupied orbitals and less dependent on the size of the active space.