Response-selective stopping requires cancellation of only one component of a multicomponent action. While research has investigated how delays to the continuing action components ("stopping interference") can be attenuated by way of contextual cues of the specific stopping demands ("foreknowledge"), little is known of the underlying neural mechanisms. Twenty-seven, healthy, young adults undertook a multicomponent stop-signal task. For two thirds of trials, participants responded to an imperative (go) stimulus (IS) with simultaneous button presses using their left and right index fingers. For the remaining one third of trials, the IS was followed by a stop-signal requiring cancellation of only the left, or right, response. To manipulate foreknowledge of stopping demands, a cue preceded the IS that informed participants which hand might be required to stop (proactive) or provided no such information (reactive). Transcranial magnetic stimulation (TMS) assessed corticospinal excitability (CSE) as well as short- and long-interval interhemispheric inhibition (SIHI, LIHI) between the primary motor cortices. Proactive cues reduced, but did not eliminate, stopping interference relative to the reactive condition. Relative to TMS measures at cue onset, decreases in CSE (both hands and both cue conditions) and LIHI (both hands, proactive condition only) were observed during movement preparation. During movement cancellation, LIHI reduction in the continuing hand was greater than that in the stopping hand and greater than LIHI reductions in both hands during execution of multicomponent responses. Our results indicate that foreknowledge attenuates stopping interference and provide evidence for a novel role of LIHI, mediated via prefrontal regions, in facilitating continuing action components.