Summary: Most differential equations found in chemical reaction networks (CRNs) have the form: \({\text d}x/{\text d}t= f(x)= Sv(x),\) where \(x \geq 0\), that is, \(x\) lies in the nonnegative orthant \({\mathbb{R}_{\geq 0}^d}\), where \(S\) is a real \(d \times d^{\prime}\) matrix (stoichiometric matrix) and \(v\) is a column vector consisting of \(d^{\prime}\) 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. J. W. Helton et al. [SIAM J. Matrix Anal. Appl. 31, 732–754 (2009; Zbl 1191.15023)] 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 \(S\), 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 is given. The Jacobian for this CRN based on \({\widehat S}\) has a sign pattern. The equilibria for the \(S\) and the \({\widehat S}\) based CRN are in exact one to one correspondence with each equilibrium \(e\) for the original CRN gotten from an equilibrium \({\widehat e}\) 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 \({\widehat e}\) 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.