Sidman (1994) noted that the existence of a member that is common to more than one class may produce either class merger (union) or class intersection. A multiple-selection, matching-to-sample test was developed to examine the conditions under which these outcomes occur. Test trials each required three conditional discriminations involving selection or rejection of comparison stimuli under control of samples representing two categories. Test results obtained from an initial group of typical adults using familiar stimuli (DOG and BIRD, pictures of dogs and birds and relevant printed breed names (e.g., DALMATIAN, RETRIEVER) showed the conditional stimulus control best described as intersection. For example, the word DALMATIAN provided the context for selecting the dalmatian but not the retriever picture. However, these results may have depended on the participants' verbal history as English speakers. Would conditional-discrimination training with overlapping sets of laboratory-generated stimuli also result in intersection? Naive typical adults were assigned to one of three different training conditions. Like the participants tested with familiar stimuli, these participants demonstrated highly reliable test outcomes best described as showing class intersection, regardless of training condition. These findings begin to elucidate the necessary and sufficient conditions for establishing complex category-like classes of stimuli.