We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water are rigorously derived from density functionals belonging to differ- ent rungs across Jacob’s ladder of approximations within density functional theory (MB-DFT) as well as from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual many-body contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the many-body formalism, by using density-corrected functionals that provide a more consistent representation of each individual many-body contribution. This is demonstrated through the development of a MB-DFT PEF derived from density-corrected PBE-D3 data, which more accurately reproduce the corresponding ab initio results.