For general multiple chemical equilibria it is shown that both the Hessian determinant and the sensitivity coefficients may be presented as sums of contributions coming from two distinct classes of reactions, which we call Hessian and non-Hessian response equilibria (HEQs and NHEQs, respectively), and pairs thereof. This approach is shown to be equivalent to another one in which the Hessian determinant and the sensitivity coefficients are treated in terms of contributions coming solely from HEQs and their pairwise interactions. The results obtained in this work hold irrespective of the type of kinetics (linear or nonlinear) by means of which the equilibrium state is achieved.