Fragment-based approximations provide the means to address dramatically larger systems sizes using quantum chemistry calculations. In recent work, we have pursued a stripped-down n-body expansion that makes no attempt at classical electrostatic embedding, as a robust means to converge fragment-based calculations to a well-defined supersystem limit, at essentially arbitrary levels of electronic structure theory including arbitrary basis sets. In the present work, we have extended this approach to protein-ligand interaction energies ∆E int , exploring the affect of distance cutoffs (both for the nbody terms and for the enzymatic model itself), and considering up to four-body terms. These considerations are unprecedented in studies of this kind. As in previous work on enzyme thermochemistry, we aim to present results that are fully converged with respect to the size of the enzyme model, while systematically testing the effects of basis set and higher n-body interactions. Our goal is to present robust protocols that can be widely deployed with relatively minor modifications, using a new software framework called Fragme∩t. For non-covalent binding of small ligands with fewer than 20 atoms to T4 lysozyme proteins, we are able to achieve remarkable accuracy for ∆E int , as assessed by comparison to a conventional supramolecular calculation at the same level of theory. Fragmentation errors are smaller than 0.01 kcal/mol/fragment, in converged enzyme models with 1,000+ atoms. This level of fidelity is an order-of-magnitude better than the very conservative standard of 0.1 × (3/2)k B T that has been suggested for fragment-based ab initio molecular dynamics simulations. This can be achieved in a total computing time (aggregated across all processors) that is only a tiny fraction of what is required for a conventional supersystem calculation at the DFT level. The cost is also small in comparison to supramolecular calculations using semi-empirical models.