  We find that the chemical abundances and dynamics of APOGEE and GALAH stars
in the local stellar halo are inconsistent with a scenario in which the inner
halo is primarily composed of debris from a single, massive, ancient merger
event, as has been proposed to explain the Gaia-Enceladus/Gaia Sausage (GSE)
structure. The data contains trends of chemical composition with energy which
are opposite to expectations for a single massive, ancient merger event, and
multiple chemical evolution paths with distinct dynamics are present. We use a
Bayesian Gaussian mixture model regression algorithm to characterize the local
stellar halo, and find that the data is best fit by a model with four
components. We interpret these components as the VRM, Cronus, Nereus, and
Thamnos; however, Nereus and Thamnos likely represent more than one accretion
event because the chemical abundance distributions of their member stars
contain many peaks. Although the Cronus and Thamnos components have different
dynamics, their chemical abundances suggest they may be related. We show that
the distinct low and high alpha halo populations from Nissen & Schuster (2010)
are explained by VRM and Cronus stars, as well as some in-situ stars. Because
the local stellar halo contains multiple substructures, different popular
methods of selecting GSE stars will actually select different mixtures of these
substructures, which may change the apparent chemodynamic properties of the
selected stars. We also find that the Splash stars in the solar region are
shifted to higher v_phi and slightly lower [Fe/H] than previously reported.
