Reflexivity entails that an organism can match a stimulus to itself (“A=A”) without direct training. Reflexivity is typically studied in identity matching-to-sample tasks wherein subjects are first presented with a sample stimulus in the middle position and trained to select the same stimulus from two comparison stimuli that are subsequently presented in the side positions. However, when the position of the comparisons is altered, nonhuman animals often revert to responding at chance levels, suggesting that they encode the location of stimuli together with their identity as part of the functional stimulus. This might hamper generalization of the task to novel stimuli (i.e., generalized identity matching-to-sample), which would be an observation of reflexivity. To test whether the use of multiple locations facilitates generalized identity matching-to-sample in rats, we used an olfactory matching-to-sample task. Two rats received training in which the location of the stimuli varied randomly. The speed with which they learned to match identical odors and the generalization to new stimuli was compared with two rats that received standard matching-to-sample training in which the location of the stimuli was fixed. We observed generalized identity matching-to-sample in two rats that could not be explained by reinforcement recency. However, we found no evidence that the use of multiple locations facilitated generalized identity matching-to-sample.