Cross-Lingual Prompt Steerability: Towards Accurate and Robust LLM Behavior across Languages

System prompts provide a lightweight yet powerful mechanism for conditioning large language models (LLMs) at inference time. While prior work has focused on English‑only settings, real‑world deployments benefit from a single prompt that operates reliably across languages. This paper presents a comprehensive study of how different system prompts steer models toward accurate and robust cross-lingual behavior. We propose a unified four-dimensional evaluation framework to assess system prompts in multilingual environments. Through experiments on five languages, three LLMs, and three benchmarks, we uncover that certain prompt components, such as CoT, emotion, and scenario, correlate with robust multilingual behavior. We develop a prompt optimization framework for multilingual settings and show it can automatically discover prompts that improve all metrics by 5-10%. Finally, we analyze over 10 million reasoning units and find that more performant system prompts induce more structured and consistent reasoning patterns, while reducing unnecessary language-switching. Together, we highlight system prompt optimization as a scalable path to accurate and robust multilingual LLM behavior.