Abstract: Multimodal objects can require different partitions under different instructions, as when products in an e-commerce catalog are grouped by color, material, or both. Retrieval-oriented embeddings may not recover these partitions, while generative clustering often relies on intermediate descriptions or iterative decisions. This paper presents CIM-Embed, a framework for learning instruction-conditioned multimodal embeddings for clustering. Supervised contrastive learning uses same-group positives and negatives from other groups, optionally including other tasks; heterogeneous structured batches accommodate tasks with different group counts. At inference, the model maps each object's image, text, and instruction directly to an embedding; HDBSCAN then forms a partition without the ground-truth cluster count. We construct ProductMIC from product metadata in Amazon Reviews 2023, comprising training data and an evaluation benchmark for instruction-conditioned clustering. The benchmark contains 5,373 products and 449 single-attribute and compositional grouping tasks spanning 50 leaf categories excluded from our training. With full-dimensional embeddings and HDBSCAN, direct within-task SupCon training achieves a mean per-task V-measure of 95.01, compared with 53.06 for WeMM 9B, the strongest general-purpose embedding baseline evaluated. Frozen product-trained encoders also improve out-of-domain conditional grouping, while controlled transfer experiments distinguish partition transfer from instruction response. We will release the code and dataset upon acceptance.