  Most differential equations found in chemical reaction networks (CRNs) have
the form $dx/dt=f(x)= Sv(x)$, where $x$ lies in the nonnegative orthant, where
$S$ is a real matrix (the stoichiometric matrix) and $v$ is a column vector
consisting of real-valued functions having a special relationship to $S$. Our
main interest will be in the Jacobian matrix, $f'(x)$, of $f(x)$, in particular
in whether or not each entry $f'(x)_{ij}$ has the same sign for all $x$ in the
orthant, i.e., the Jacobian respects a sign pattern. In other words species
$x_j$ always acts on species $x_i$ in an inhibitory way or its action is always
excitatory.
  In Helton, Klep, Gomez we gave necessary and sufficient conditions on the
species-reaction graph naturally associated to $S$ which guarantee that the
Jacobian of the associated CRN has a sign pattern. In this paper, given $S$ we
give a construction which adds certain rows and columns to $S$, thereby
producing a stoichiometric matrix $\widehat S$ corresponding to a new CRN with
some added species and reactions. The Jacobian for this CRN based on $\hat S$
has a sign pattern. The equilibria for the $S$ and the $\hat S$ based CRN are
in exact one to one correspondence with each equilibrium $e$ for the original
CRN gotten from an equilibrium $\hat e$ for the new CRN by removing its added
species. In our construction of a new CRN we are allowed to choose rate
constants for the added reactions and if we choose them large enough the
equilibrium $\hat e$ is locally asymptotically stable if and only if the
equilibrium $e$ is locally asymptotically stable. Further properties of the
construction are shown, such as those pertaining to conserved quantities and to
how the deficiencies of the two CRNs compare.
