Current theories describe cognitive control as a dynamic balance between two antagonistic control functions, namely cognitive stability and flexibility. Recent evidence suggests that this balance between these control modes is modulated by changing reward prospects on the one side and contextual parameters on the other. In the present study, we aim to investigate how both factors interact. In a between-subjects design, we manipulated the context by the ratio of free- to forced-choice trials (80:20, 50:50, 20:80) in a hybrid task-switching paradigm, combining forced- and free-choice task switching. In addition, two reward magnitudes changed randomly from trial to trial. Results showed an overall increase in voluntary switch rate (VSR) with increasing forced-choice frequency, demonstrating a robust context effect. Moreover, the trial-by-trial reward manipulation interacted with this global context effect: with a stability bias (80% free:20% forced), only an increase in reward expectation increased VSR, whereas with a more flexible global bias (in the 50:50 or 20:80 conditions) VSR increased when reward expectation changed and reduced when reward expectation remained high. Taken together, results suggest that the cognitive system is able to adapt to global context parameters and to respond to rapid changes in reward expectation at the same time.