  Binary neutron star mergers produce massive, hot, rapidly differentially
rotating neutron star remnants; electromagnetic and gravitational wave signals
associated with the subsequent evolution depend on the stability of these
remnants. Stability of relativistic stars has previously been studied for
uniform rotation and for a class of differential rotation with monotonic
angular velocity profiles. Stability of those equilibria to axisymmetric
perturbations was found to respect a turning point criterion: along a constant
angular momentum sequence, the onset of unstable stars is found at maximum
density less than but close to the density of maximum mass. In this paper, we
test this turning point criterion for non-monotonic angular velocity profiles
and non-isentropic entropy profiles, both chosen to more realistically model
post-merger equilibria. Stability is assessed by evolving perturbed equilibria
in 2D using the Spectral Einstein Code. We present tests of the code's new
capability for axisymmetric metric evolution. We confirm the turning point
theorem and determine the region of our rotation law parameter space that
provides highest maximum mass for a given angular momentum.
