Sketching algorithms are considered as promising solutions for answering approximate query on massive data stream. In real scenarios, a large number of problems can be abstracted as subset query over multiple attributes. Existing sketches are designed for query on single attributes, and therefore are inefficient for query on multiple attributes. In this work, we propose Hyper-USS, an innovative sketching algorithm that supports subset query over multiple attributes accurately and efficiently. To the best of our knowledge, this work is the first sketching algorithm designed to answer approximate query over multi-attribute data stream. We utilize the key technique, Joint Variance Optimization, to guarantee high estimation accuracy on all attributes. Experiment results show that, compared with the state-of-the-art (SOTA) sketches that support subset query on single attributes, Hyper-USS improves the accuracy by 16.67X and the throughput by 8.54X. The code is open-sourced at Github.