The cutoff recognizes that at long-range the n-body terms can be understood from multipole expansions and, notably, from many-body polarization. In the present work we did not examine in detail the effect of reducing the cutoff for the 4-b term and thereby reducing the number of 4-b terms. This is certainly something we plan to examine in detail in follow-up work. In addition, it is clear that the MB-PES can exploit straightforward parallelization which can also increase the speed of evaluation. Both aspects have been examined for our MB q-AQUA water potential and the interested reader is referred to those references for details.