We have the task of measuring kinetic parameters of an oxidase reaction that has a $K_M$ of about $2 \,\text{mM}$. For that, we want to use a fluorescence assay based on Amplex Red. The latter is a fluorogenic substance of an upper detection limit of $5 \, \mu \text{M}$. At higher concentrations, the inner filter effect causes non-linear behaviour.
Usually, we would use substrate and fluorophore concentrations of a similar range of the $K_M$ value. Obviously, we cannot do that here, as the fluorophore concentration would be way above the upper detection limit. This led us to the idea of reducing the substrate, fluorophore, and enzyme concentration by the same factor to do measurements in a micromolar range. Later we could simply scale up the results.
We doubt that this method is possible as the Michaelis-Menthen kinetics never look at the ratio between substrates and enzyme, but only regard absolute substrate concentrations.
So our question is if the proposed method is in fact not applicable and if so, what your suggestions would be?