An accurate model of electronic structure, within the framework of cumulant functional theory, that combines density matrix functional theory and a two-electron density functional is proposed. The approximate parameterization of the two-electron density matrix (2-RDM) is designed to treat so-called potential dependent correlation. Whereas, the two-electron density functional (TDF) is designed to capture the short-range component of so-called universal correlation. Parameterization of the 2-RDM involves including the leading-order terms that contribute to inter and intra-pair correlation while satisfying constraints of \(N\)-representability. A TDF allows for the precise accounting of all energetic consequences of any proposed electron-electron interaction ansatz ({\it i.e.}~kinetic, electron-electron potential and nucleus-electron potential). The advantages and challenges of such approaches will be discussed as well as preliminary results for atoms and small molecules.