Successful multitasking requires subjects to flexibly activate task goals important to accomplish the task at hand. However, the neural mechanisms underlying goal activation in multitasking are unknown. Based on neurobiological models of action selection, we expected that the extent to which task-goals are processed with some overlap that strongly depends on striatal structures. Therefore, we applied a stop-change paradigm to examine multitasking using fMRI and manipulated the delay between the stop stimulus and the subsequently following change signal towards a new GO response (stop-change delay; SCD). The manipulation of the SCD was introduced to achieve varying amounts of overlap of the two task-goals (stop goal, change goal). This manipulation allowed the calculation of a stop-change delay-reaction time function (SCD-RT function), with the slope of this function, reflecting on the degree of overlap between the stop and the change goal. Data analysis revealed that change trials, independent of their SCD, showed an activation pattern encompassing frontal and parietal cortical regions. Contrasting the two main SCD (long vs. short SCD) conditions with each other showed a stronger BOLD (blood oxygenation level dependent) signal activation of the caudate and the right inferior frontal gyrus in trials with a long SCD compared to trials with a short SCD. Follow-up analyses showed that activation differences of the caudate between the two SCDs drive the effect. Integrating the fMRI data with the slope of the SCD-RT function indicated that the degree of overlap of stop and change processes is determined by the degree of striatal activation on a serial-to-parallel continuum. In conclusion, the findings acknowledge the role of the basal ganglia as an important structure determining action selection processes via a network of neocortical and striatal structures, in terms of an extended multiple demand system.