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The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller–Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod–Teller–Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol−1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol−1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is −54.01 kJ mol−1, compared to an estimated experimental value of −55.3 ± 2.2 kJ mol−1.