There is now much evidence that humans have multiple memory systems, and evidence is also building that other cognitive processes are mediated by multiple systems. Even so, several recent articles have questioned the existence of multiple cognitive systems, and a number of these have based their arguments on results from state-trace analysis. State-trace analysis was not developed for this purpose but, rather, to identify data sets that are consistent with variation in a single parameter. All previous applications have assumed that state-trace plots in which the data fall on separate curves rule out any model in which only a single parameter varies across the two tasks under study. Unfortunately, this assumption is incorrect. Models in which only one parameter varies can generate any type of state-trace plot, as can models in which two or more parameters vary. In addition, it is straightforward to show that both single-system and multiple-systems models can generate state-trace plots that are considered in the literature to be consistent with either one or multiple cognitive systems. Thus, without additional information, there is no empirical state-trace plot that supports any inferences about the number of underlying parameters or systems.