How can we distinguish positive cooperativity from auto-catalysis in enzyme kinetics?

Different graphical plots involving the catalytic rate with the (initial) substrate concentration exist in the enzyme kinetics literature to estimate the reaction constants. But, none of these standard plots can unambiguously distinguish between the two important mechanisms of rate enhancement: positive cooperativity among the active sites of an oligomeric enzyme and auto-catalysis of the intermediate complex of an enzyme with a single active site. We achieve this distinction here by providing a nice linear plot for the latter. Importantly, to accomplish this task, no extra information other than the steady-state rate as a function of substrate concentration is required.