Distance-based thresholding has often been considered as a means to tame the combinatorics of MBE(n), but for high-order expansions this effectively limits the subsystems to nearest-neighbors only. This may omit cooperative dipolar interactions that can sometimes cause energetically-important terms to persist at longer length scales. Within a distance-based screening approach, these terms must either be omitted (at the expense of accuracy), or else the distance cutoff must be relaxed, which is detrimental to efficiency. Distance-based screening must furthermore be done carefully (by means of smooth cutoffs) in order to avoid introducing discontinuities in potential energy surfaces. Ab initio molecular dynamics simulations are quite sensitive to small inconsistencies between the energy and forces, which can lead to catastrophic failure to conserve energy. In previous work, we introduced an energy-screened MBE(3) method in which a polarizable force field was used to screen the three-body terms. The target level of ab initio theory was applied to trimer IJK only if