Recently, we [Kleinsorge & Heuer (1999) Psychological Research, 62, 300-312] introduced the notion of generalizing switching operations to account for a characteristic pattern of shift costs that can be observed when participants have to shift between four tasks that result from an orthogonal combination of the two binary task dimensions kind of judgment (numerical vs spatial) and judgment-to-response mapping (compatible vs incompatible). Specifically, while a change of the kind of judgment always results in costs, a change of mapping results in costs only when the kind of judgment is repeated, but results in benefits when the kind of judgment changes as well. In Experiment 1, we replicated and extended this finding with a combination of two spatial kinds of judgment that were more similar to each other and were more unlikely to result in build-in dependencies of the two task dimensions. In Experiment 2, we extended this design to a combination of nine tasks that resulted from a factorial combination of two three-valued task dimensions. In this experiment, shift costs grew monotonically with the number of task dimensions on which a change took place. This outcome is consistent with the assumption that a generalizing switching operation is a forward-acting process that requires a specific target value to switch to.