Multimodal fusion addresses the problem of analyzing spoken words in the multimodal context, including visual expressions and prosodic cues. Even when multimodal models lead to performance improvements, it is often unclear whether bimodal and trimodal interactions are learned or whether modalities are processed independently of each other. We propose Multimodal Residual Optimization (MRO) to separate unimodal, bimodal, and trimodal interactions in a multimodal model. This improves interpretability as the multimodal interaction can be quantified. Inspired by Occam’s razor, the main intuition of MRO is that (simpler) unimodal contributions should be learned before learning (more complex) bimodal and trimodal interactions. For example, bimodal predictions should learn to correct the mistakes (residuals) of unimodal predictions, thereby letting the bimodal predictions focus on the remaining bimodal interactions. Empirically, we observe that MRO successfully separates unimodal, bimodal, and trimodal interactions while not degrading predictive performance. We complement our empirical results with a human perception study and observe that MRO learns multimodal interactions that align with human judgments.