A central focus of cognitive neuroscience is identification of the neural codes that represent stimulus dimensions. One common theme is the study of whether dimensions, such as color and shape, are encoded independently by separate pools of neurons or are represented by neurons conjointly tuned for both properties. We describe an application of functional magnetic resonance imaging (fMRI) adaptation to distinguish between independent and conjoint neural representations of dimensions by examining the neural signal evoked by changes in one versus two stimulus dimensions and considering the metric of two-dimension additivity. We describe how a continuous carry-over paradigm may be used to efficiently estimate this metric. The assumptions of the method are examined as are optimizations. Finally, we demonstrate that the method produces the expected result for fMRI data collected from ventral occipitotemporal cortex while subjects viewed sets of shapes predicted to be represented by conjoint or independent neural tuning.