A growing methodology, known as the systems factorial technology (SFT), is being developed to diagnose the types of information-processing architectures (serial, parallel, or coactive) and stopping rules (exhaustive or self-terminating) that operate in tasks of multidimensional perception. Whereas most previous applications of SFT have been in domains of simple detection and visual-memory search, this research extends the applications to foundational issues in multidimensional classification. Experiments are conducted in which subjects are required to classify objects into a conjunctive-rule category structure. In one case the stimuli vary along highly separable dimensions, whereas in another case they vary along integral dimensions. For the separable-dimension stimuli, the SFT methodology revealed a serial or parallel architecture with an exhaustive stopping rule. By contrast, for the integral-dimension stimuli, the SFT methodology provided clear evidence of coactivation. The research provides a validation of the SFT in the domain of classification and adds to the list of converging operations for distinguishing between separable-dimension and integral-dimension interactions. (Contains 9 figures, 7 tables, and 7 footnotes.)