The present chapter describes an alternative approach to EDA for intermolecular interactions that is not based on DFT but rather on many-body theory, and aims to compute the interaction energy directly from first principles (and not by energy difference), with quantitative accuracy. That approach, which is known as symmetry-adapted perturbation theory (SAPT), has a long history in quantum chemistry that is not reviewed here. Rather, the present work examines a relatively new family of hybrid methods that are built upon the SAPT framework but substitute alternative models for dispersion, in place of perturbation theory. This is done in the interest of achieving quantitative accuracy at a cost that is cubic-scaling [O(N 3 )] with system size, and thus comparable in cost to DFT. These methods are known collectively as "extended" (X)SAPT, originally built upon a combination of SAPT with the "XPol" self-consistent charge embedding procedure. XSAPT has been developed in the Herbert group since 2010, with the goal of providing qualitative insight (via a well-defined EDA) that is built atop a method that delivers quantitative accuracy, and the philosophy that physical insight should be independent of the ever-evolving milieu of density-functional approximations.