The multimodal model has demonstrated promise in histopathology. However, most multimodal models are based on H\&E and genomics, adopting increasingly complex yet black-box designs. In our paper, we propose a novel interpretable multimodal framework named SHAP-CAT, which uses a Shapley-value-based dimension reduction technique for effective multimodal fusion. Starting with two paired modalities -- H\&E and IHC images, we employ virtual staining techniques to enhance limited input data by generating a new clinical-related modality. Lightweight bag-level representations are extracted from image modalities and a Shapley-value-based mechanism is used for dimension reduction. For each dimension of the bag-level representation, attribution values are calculated to indicate how changes in the specific dimensions of the input affect the model output. In this way, we select a few top important dimensions of bag-level representation for each image modality to late fusion. Our experimental results demonstrate that the proposed SHAP-CAT framework incorporating synthetic modalities significantly enhances model performance, yielding a 5\% increase in accuracy for the BCI, an 8\% increase for IHC4BC-ER, and an 11\% increase for the IHC4BC-PR dataset.