We develop a framework for optimizing a novel approach to extending the linear range of bioanalytical systems and biosensors by utilizing two enzymes with different kinetic responses to the input chemical as their substrate. Data for the flow injection amperometric system devised for detection of lysine based on the function of L-lysine-alpha-oxidase and lysine-2-monooxygenase are analyzed. Lysine is a homotropic substrate for the latter enzyme. We elucidate the mechanism for extending the linear response range and develop optimization techniques for future applications of such systems.