Here, we present a combination of MFCC with a second-order MBE, which is based on the MOBE by Mayhall and Raghavachari and which requires only calculations for the original MFCC fragments and cap molecules and for pairs of these. We demonstrate how such a scheme can handle the ACE-NME caps while at the same time accounting for many-body effects. We show that our scheme significantly improves the total energies of proteins compared to both the conventional MFCC approach and to a two-body expansion for MFCC with hydrogen caps.