The peroxidase-oxidase oscillating reaction was the first (bio)chemical reaction to show chaotic behaviour. The reaction is rich in bifurcation scenarios, from period-doubling to peak-adding mixed mode oscillations. Here, we study a state-of-the-art model of the peroxidase-oxidase reaction. Using the model, we report systematic numerical experiments exploring the impact of changing the enzyme concentration on the dynamics of the reaction. Specifically, we report high-resolution phase diagrams predicting and describing how the reaction unfolds over a quite extended range of enzyme concentrations. Surprisingly, such diagrams reveal that the enzyme concentration has a huge impact on the reaction evolution. The highly intricate dynamical behaviours predicted here are difficult to establish theoretically due to the total absence of an adequate framework to solve nonlinearly coupled differential equations. But such behaviours may be validated experimentally.