Large Language Models (LLMs) have revolutionized natural language processing but remain vulnerable to jailbreak attacks, especially multi-turn jailbreaks that distribute malicious intent across benign exchanges and bypass alignment mechanisms. Existing approaches often explore the adversarial space poorly, rely on hand-crafted heuristics, or lack systematic query refinement. We present NEXUS (Network Exploration for eXploiting Unsafe Sequences), a modular framework for constructing, refining, and executing optimized multi-turn attacks. NEXUS comprises: (1) ThoughtNet, which hierarchically expands a harmful intent into a structured semantic network of topics, entities, and query chains; (2) a feedback-driven Simulator that iteratively refines and prunes these chains through attacker-victim-judge LLM collaboration using harmfulness and semantic-similarity benchmarks; and (3) a Network Traverser that adaptively navigates the refined query space for real-time attacks. This pipeline uncovers stealthy, high-success adversarial paths across LLMs. On several closed-source and open-source LLMs, NEXUS increases attack success rate by 2.1% to 19.4% over prior methods. Code: https://github.com/inspire-lab/NEXUS