For all three values of M , the number of fragments decreases as the screening on the lower-level fragments becomes stricter (larger τ 3 ). A sharp drop in accuracy for MBE(3) is again observed for τ 3 > 0.1 kcal/mol [Fig. ], which remains evident for MBE(4) using either M = 0 [Fig. ] or M = 1 [Fig ]. This indicates that addition of four-body terms does not obfuscate the screening that is performed at the three-body level. However, the choice M = 2 [Fig 6(d)] does appear to interfere with the three-body screening, leading to a significant growth in the number of subsystems [Fig 6(h)]. For M = 2, errors do remain tightly clustered even for τ 3 > 0.1 kcal/mol, so in some sense this approach is able to inoculate the method against a poor choice of τ 3 , yet that security comes at significant cost. Setting M = 1 and τ 3 = 0.05 kcal/mol provides a good balance between accuracy and efficiency.