We present a method for discovering patterns of selectivity in fMRI data for experiments with multiple stimuli/tasks. We introduce a representation of the data as profiles of selectivity using linear regression estimates, and employ mixture model density estimation to identify functional systems with distinct types of selectivity. The method characterizes these systems by their selectivity patterns and spatial maps, both estimated simultaneously via the EM algorithm. We demonstrate a corresponding method for group analysis that avoids the need for spatial correspondence among subjects. Consistency of the selectivity profiles across subjects provides a way to assess the validity of the discovered systems. We validate this model in the context of category selectivity in visual cortex, demonstrating good agreement with the findings based on prior hypothesis-driven methods.