The simplest way to predict London dispersion energies involving complex multiatom objects is to add separate contributions from each pair of atoms. Semiempirical, and even certain less empirical, ways to do this can be very efficient computationally and have recently been developed to a high level of sophistication, with considerable success. There are, however, effects that are not captured in this way, including surprising dependences of the dispersion energy on the number N of atoms and on separation D. Higher level quantum chemical, perturbative, and random-phase approximation (RPA)-like theories can capture these beyond pairwise effects, but at a high computational cost. Very recent simplified RPA-like approaches based on localized oscillators account for the unusual N dependence in a computationally efficient way. To proceed further, the present work proposes three physically distinct categories of nonpairwise effects (types A, B, and C) against which the performance of existing and future theories can be assessed. © 2014 Wiley Periodicals, Inc.