Antioxidant nanozymes are powerful tools to combat oxidative stress, which can be further improved by applying nanozyme mixtures of multiple enzymatic function. Here, cocktails of Prussian blue (PB) nanocubes and copper(II) exchanged ZSM-5 zeolites (CuZ) with enhanced reactive oxygen species (ROS) scavenging activity were developed. Surface functionalization of the particles was performed using polymers to obtain stable colloids, i.e., resistant to aggregation, under a wide range of experimental conditions. The nanozyme cocktails possessed advanced antioxidant properties with multiple enzyme-like functions, catalyzing the decomposition of ROS in cascade reactions. The activity of the mixture far exceeded that of the individual particles, particularly in the peroxidase assay, where an improvement of more than an order of magnitude was observed, pointing to coamplification of the enzymatic activity. In addition, it was revealed that the copper(II) site in the CuZ plays an important role in the decomposition of both superoxide radicals and hydrogen peroxide, as it directly catalyzes the former reaction and acts as cocatalyst in the latter process by boosting the peroxidase activity of the PB nanozyme. The results give important insights into the design of synergistic particle mixtures for the broad-spectrum scavenging of ROS to develop efficient tools for antioxidant treatments in both medical therapies and industrial manufacturing processes.