As large language models (LLMs) become widely adopted, ensuring their alignment with human values is crucial to prevent jailbreaks where adversaries manipulate models to produce harmful content. While most defenses target single-turn attacks, real-world usage often involves multi-turn dialogues, exposing models to attacks that exploit conversational context to bypass safety measures. We introduce MUSE, a comprehensive framework tackling multi-turn jailbreaks from both attack and defense angles. For attacks, we propose MUSE-A, a method that uses frame semantics and heuristic tree search to explore diverse semantic trajectories. For defense, we present MUSE-D, a fine-grained safety alignment approach that intervenes early in dialogues to reduce vulnerabilities. Extensive experiments on various models show that MUSE effectively identifies and mitigates multi-turn vulnerabilities. Code is available at https://anonymous.4open.science/r/MUSE-75F7.