Combining a fragmentation method based on capped or overlapping fragments with the MBE requires carefully ensuring that no double counting occurs, which can be achieved by applying the inclusion-exclusion principle . The most rigorous and general approach is provided by the generalized MBE . The Many Overlapping Body Expansion (MOBE) is more tractable, but contains some additional approximations . For a very general reformulation of MBEs for quantum-chemical fragmentation methods, we refer to Ref. .