Unlike the top-down screening method that we reported previously, which requires energy screening for every individual n-body system, the bottom-up approach propagates screening information upwards. As a result, the screening is much more aggressive (and thus the algorithm more performant) without loss of accuracy, and we find that the number of n-body subsystems naturally attenuates as n increases. As such, MBE(n) can be used without specifying a maximum order n, yet subsystem counts remain manageable. For (H 2 O) 20 , terms beyond n = 5 appear to contribute only to BSSE. In future work, this will be investigated further using larger basis sets and many-body counterpoise corrections. The software reported here makes MBE(n) into a robust tool for high-fidelity fragment-based quantum chemistry. Our open-source implementation is easy to interface with various quantum chemistry programs and can be used to prototype new fragmentation strategies. We anticipate that this implementation will lower the entry barrier to using fragmentation methods, and furthermore provide a degree of community validation that has heretofore been lacking in fragment-based quantum chemistry.