It is unclear whether cognitive and motor control are parallel and interactive or serial and independent processes. According to one view, cognitive control refers to a set of modality-nonspecific processes that act on supramodal representations and precede response modality-specific motor processes. An alternative view is that cognitive control represents a set of modality-specific operations that act directly on motor-related representations, implying dependence of cognitive control on motor control. Here, we examined the influence of response modality (vocal vs. manual) on three well-established subcomponent processes of cognitive control: shifting, inhibiting, and updating. We observed effects of all subcomponent processes in reaction times. The magnitude of these effects did not differ between response modalities for shifting and inhibiting, in line with a serial, supramodal view. However, the magnitude of the updating effect differed between modalities, in line with an interactive, modality-specific view. These results suggest that updating represents a modality-specific operation that depends on motor control, whereas shifting and inhibiting represent supramodal operations that act independently of motor control.