  One important question that interests those who work in chemical reaction
network theory (CRNT) is this: Does the system obtained from a reaction network
admit a positive equilibrium and if it does, can there be more than one within
a stoichiometric class? The higher deficiency algorithm (HDA) of Ji and
Feinberg provided a method of determining the multistationarity capacity of a
CRN with mass action kinetics (MAK). An extension of this, called
Multistationarity Algorithm (MSA), recently came into the scene tackling CRNs
with power law kinetics (PLK), a kinetic system which is more general (having
MAK systems as a special case). For this paper, we provide a computational
approach to study the multistationarity feature of reaction networks endowed
with kinetics which are non-negative linear combinations of power law functions
called poly-PL kinetics (PYK). The idea is to use MSA and combine it with a
transformation called STAR-MSC (i.e., $S$-invariant Termwise Addition of
Reactions via Maximal Stoichiometric Coefficients) producing PLKs that are
dynamically equivalent to PYKs. This leads us to being able to determinine the
multistationarity capacity of a much larger class of kinetic systems. We show
that if the transformed dynamically equivalent PLK system is multistationary
for a stoichiometric class for a set of particular rate constants, then so is
its original corresponding PYK system. Moreover, the monostationarity property
of the transformed PLK system also implies the monostationarity property of the
original PYK system.
