As cluster size increases, a systematic error emerges, in both the (H 2 O) 32 and (H 2 O) 64 calculations, that is larger than the (relatively constant) error in amongst relative energies of different clusters of the same size. To demonstrate that this systematic error is due to BSSE, we performed MBE(3) and MBE(4) calculations for a single (H 2 O) 64 isomer using the full cluster basis set, meaning that n-body subsystem calculations are carried out using the basis set of the (H 2 O) 64 supersystem. Errors in these cluster-basis calculations are plotted in Fig. ) alongside the corresponding errors obtained using the conventional subsystem basis. Use of the cluster basis reduces the error below 0.025 kcal/mol/monomer for both MBE(3) and MBE(4), whereas the use of the subsystem basis afford errors that grow with τ 3 , even when that threshold is set quite conservatively. Although the use of a supersystem basis set may not be practical in largescale calculations, in future work this can replaced with many-body counterpoise corrections. ) with M = 1, both as a function of τ 3 and reported in per-monomer units. (c) Errors for both MBE(3) and MBE(4) for one particular snapshot, in either the usual subsystem basis set (in blue) versus the full cluster basis set (in orange). (d)-(e) Mean fragment counts as a function of τ 3 .