Longstanding conventional wisdom dictates that the widely used Many-Body Expansion (MBE) converges rapidly by the four-body term when applied to large chemical systems. We have found, however, that this is not true for calculations using many common, moderate-sized basis sets such as 6-311++G** and aug-cc-pVDZ. Energy calculations performed on water clusters using these basis sets showed a deceptively small error when the MBE was truncated at the three-body level, while inclusion of four- and five-body contributions drastically increased the error. Moreover, the error per monomer increases with system size, showing that the MBE is unsuitable to apply to large chemical systems when using these basis sets. Through a systematic study, we identified the cause of the poor MBE convergence to be a many-body basis set superposition effect exacerbated by diffuse functions. This was verified by analysis of MO coefficients and the behavior of the MBE with increasing monomer-monomer separation. We also found poor convergence of the MBE when applied to valence-bonded systems, which has implications for molecular fragmentation methods. The findings in this work suggest that calculations involving the MBE must be performed using the full-cluster basis set, using basis sets without diffuse functions, or using a basis set of at least aug-cc-pVTZ quality.