However, combining the MBE with the MFCC fragmentation approach is not straightforward because of the ACE-NME caps that need to be introduced. To approximately describe two-body interactions in MFCC, a pairwise energy correction based on specific parts of the fragment density matrices has been proposed . Similarly, for fragmentation methods with overlapping fragments, such as the molecular tailoring approach by Gadre and coworkers, specific missing two-body and three-body contributions can be added . Very general schemes for systematically including many-body effects have also been developed. The Generalized Many Body Expansion (GMBE) by Richard and Herbert provides a very rigorous and general approach for combining overlapping fragments with the MBE . The Many Overlapping Body Expansion (MOBE) by Mayhall and