Such general fragmentation schemes can be applied to proteins and allow for their accurate quantum-chemical treatment, provided that sufficient level of many-body contributions is included. However, this might require a large number of fragment calculations, which need to be addressed by introducing additional approximations. Liu and Herbert applied the GMBE to proteins and included up to four-body contributions, while applying a pair-pair approximation . In Ref. 52, up to three-body contributions were included to obtain accurate total energies of proteins. Here, we do not aim reaching the accuracy of such generalized many-body schemes, but instead want to efficiently improve upon the simple and widely-used MFCC scheme by including two-body terms consistently.