Many-body dispersion has gained considerable attention over the past decade, particularly for condensed phase systems. However, quantitatively accurate studies of many-body dispersion have only recently become feasible due to challenges in reliability and accuracy. Currently available methodologies for calculating many-body dispersion have been challenged, with recent evidence suggesting, for example, that dispersion- corrected density functional theory (DFT) schemes cannot consistently predict many-body dispersion accurately. This study evaluates many-body dispersion energies using a composite approach that employs singles and doubles coupled cluster theory with perturbative/noniterative triples, CCSD(T), combined with an extrapolation to the complete basis set (CBS) limit. The combined CCSD(T)/CBS approach is applied to Ar-n and (H2O)(n), n = 3-10, clusters, and a new data set called S22(3), which includes trimers generated based on the S22 data set. In these systems, the many-body dispersion provides a very small contribution to the total interaction energy of all of the systems studied, generally 3% or less of the total interaction energy. Two-body dispersion is the dominant dispersion contribution and many-body dispersion contributes no more than 5.7% of the total dispersion energy, generally staying below 2%.