We revisit two-step mass-balance models of biological processes as met to describe numerous biological systems including the anaerobic digestion or the nitrification process in view of its global stabilization. We show that when a bi-stability occurs, it can be possible to globally stabilize the dynamics toward an unique positive equilibrium by increasing the dilution rate. We give sufficient conditions on the growth functions of the model for this situation to appear. This illustrates that for biological multi-step reactional systems, increasing the residence time (e.g. decreasing the input flow rate) may not be the only way to stabilize the dynamics.