Response inhibition is a key attribute of human executive control. Standard stop-signal tasks require countermanding a single response; the speed at which that response can be inhibited indexes the efficacy of the inhibitory control networks. However, more complex stopping tasks, where one or more components of a multi-component action are cancelled (i.e., response-selective stopping) cannot be explained by the independent-race model appropriate for the simple task (Logan and Cowan, 1984). Healthy human participants (n=28; 10 male; 19-40 years) completed a response-selective stopping task where a `go’ stimulus required simultaneous (bimanual) button presses in response to left and right pointing green arrows. On a subset of trials (30%) one, or both, arrows turned red (constituting the stop signal) requiring that only the button-press(es) associated with red arrows be cancelled. Electromyographic recordings from both index fingers (first dorsal interosseous) permitted voluntary motor responses that resulted in overt button presses, and activity that was cancelled prior to an overt response (i.e., partial, or covert, responses), to be assessed. We propose a simultaneously inhibit and start (SIS) model that extends the independent race model and provides a highly accurate account of response-selective stopping data. Together with fine-grained EMG analysis, our model-based analysis offers converging evidence that the selective-stop signal simultaneously triggers a process that stops the bimanual response and triggers a new unimanual response corresponding to the green arrow. Our results require a reconceptualization of response-selective stopping and offer a tractable framework for assessing such tasks in healthy and patient populations.