To describe singly-ionized states of molecular clusters we devised an effective Hamiltonian approach that combines (1) accurate monomer ionization potentials from many-electron wave functions with (2) polarization shifts and (3) effective monomer couplings obtained from a simple one-electron approach (the superposition-of-fragment-states (SFS) method [Valeev et al., J. Am. Chem. Soc., 2006, 128, 9882]). The accuracy of the intermolecular coupling parameters evaluated with SFS Hartree–Fock (HF) and Density-Functional-Theory (DFT) variants was evaluated for several weakly-bound dimers and compared against the state-of-the-art equation-of-motion ionization-potential coupled-cluster singles and doubles (EOM-IP-CCSD) data of Krylov and co-workers. The SFS–HF method produces coupling integrals accurate to a few percent, whereas SFS–DFT predictions are substantially worse. A hybrid approach combining SFS–HF couplings and shifts with EOM-IP-CCSD ionization potentials of monomers (denoted as SFS-EOM-IP-CCSD) was applied to ionized states of two conformers of a benzene dimer and ten representative DNA base pairs. The 16 considered SFS-EOM-IP-CCSD ionization potentials of the benzene dimer differed from the reference EOM-IP-CCSD IPs of Krylov and co-workers [Pieniazek et al., J. Chem. Phys. 2007, 127, 044317; Bravaya et al., Phys. Chem. Chem. Phys. 2010, 12, 2261] by less than 0.1 eV on average, and at most by 0.2 eV. For the DNA base pairs the mean absolute (median) deviation of the SFS-EOM-IP-CCSD IPs was 0.27 (0.23) eV; several deviations for non-Koopmans states were as large as 0.9 eV. The SFS-EOM-IP-CCSD method can be readily applied to large molecular clusters with computational effort scaling cubically with the size of the cluster.