  The X-ray spectra of active galactic nuclei (AGNs) often exhibit an excess of
emission above the primary power-law at energies <~ $2$ keV. Two models for the
origin of this `soft excess' are ionized relativistic reflection from the inner
accretion disc and Comptonization of thermal emission in a warm corona. Here,
we introduce reXcor, a new AGN X-ray ($0.3$-$100$ keV) spectral fitting model
that self-consistently combines the effects of both ionized relativistic
reflection and the emission from a warm corona. In this model, the accretion
energy liberated in the inner disc is distributed between a warm corona, a
lamppost X-ray source, and the accretion disc. The emission and ionized
reflection spectrum from the inner $400$ $r_g$ of the disc is computed,
incorporating the effects of relativistic light-bending and blurring. The
resulting spectra predict a variety of soft excess shapes and sizes that depend
on the fraction of energy dissipated in the warm corona and lamppost. We
illustrate the use of reXcor by fitting to the joint XMM-Newton and NuSTAR
observations of the Seyfert 1 galaxies HE 1143-1820 and NGC 4593, and find that
both objects require a warm corona contribution to the soft excess. Eight
reXcor table models, covering different values of accretion rate, lamppost
height and black hole spin, are publicly available through the XSPEC website.
Systematic use of reXcor will provide insight into the distribution of energy
in AGN accretion flows.
