Compound cue retrieval is a computational model of a mediated route for response selection in task-switching situations. In previous studies, the model has been shown to account for response congruency effects when switching between two tasks, where response congruency reflects the degree of match between relevant and irrelevant task responses associated with a target stimulus. In the present study, the author derived a model prediction of graded response congruency effects in situations involving three tasks. The predicted pattern was observed for both response time and error rate in an experiment in which numerical categorization tasks were performed on single-digit targets. Implications for understanding response congruency effects and for developing models of task-switching performance are discussed.