Psychological research increasingly relies on high-dimensional data, yet it remains challenging to determine whether patterns of representation are independent across experimental contexts. Traditional multivariate approaches, such as decoding, are sensitive to pattern differences but do not directly test factorial hypotheses. In contrast, analysis of variance (ANOVA) provides inferential clarity but is limited to univariate measures. To address this gap, we introduce Multivariate Interaction Classification (MIC), a framework that combines the logic of factorial interaction tests with the sensitivity of multivariate pattern analysis. MIC evaluates representational independence by comparing within-context and cross-context decoding performance. Through simulation studies, we show that MIC reliably distinguishes modality-specific, modality-general, and hybrid representational structures. We then validate the method with affective ratings of gustatory and auditory stimuli, demonstrating how MIC can reveal the coexistence of specific and general codes. By providing a statistically grounded and easily implemented tool, MIC enables researchers to move beyond descriptive decoding toward confirmatory tests of representational hypotheses. All code and materials are openly available to ensure transparency and reproducibility.