Positive feedback loops can produce multistability, resulting in different phenotypic states. However, many transcription networks contain counteracting positive and negative feedbacks. Here we explore the dynamics of an interlinked positive and negative feedback motif based on the galactose-uptake control system of Saccharomyces cerevisiae modified to make the strength of each feedback externally controllable. Our results show that although the positive feedback loop determines the range of bistability and the width of the regions where intermediate activation is possible, the transition rates between states are mostly sensitive to the negative feedback strength. Thus, our results suggest that the function of the negative loop in this motif is to allow separate tuning of the range and transition rates between phenotypic states. This could enhance fitness by allowing improved matching of the stochastic switching to the frequency of environmental changes.