This research introduces STAR, a sociotechnical framework that improves on current best practices for red teaming safety of large language models. STAR makes two key contributions: it enhances steerability by generating parameterised instructions for human red teamers, leading to improved coverage of the risk surface. Parameterised instructions also provide more detailed insights into model failures at no increased cost. Second, STAR improves signal quality by matching demographics to assess harms for specific groups, resulting in more sensitive annotations. STAR further employs a novel step of arbitration to leverage diverse viewpoints and improve label reliability, treating disagreement not as noise but as a valuable contribution to signal quality.