Hidden malicious intent in multi-turn dialogue poses a growing threat to deployed large language models (LLMs). Rather than exposing a harmful objective in a single prompt, attackers can distribute their intent across multiple benign-looking turns, making defense a problem not only of whether a dialogue is harmful, but also of when intervention becomes necessary. Existing trace-level labeling approaches provide only coarse safety signals and do not identify this intervention boundary, making it difficult to distinguish timely intervention from premature refusal or a block that comes too late. This work introduces turn-level harm-enabling supervision for multi-turn defense. We define the earliest harm-enabling turn as the first point at which delivering a candidate response would make the accumulated interaction sufficient to enable harmful action. To instantiate this supervision at scale, we construct the Multi-Turn Intent Dataset (MTID), which contains adaptive attack rollouts, matched benign hard negatives, and annotations of this boundary. Using MTID, we train TurnGate, a response-aware monitor that learns when to intervene, and further optimize its policy through multi-turn reinforcement learning. Experiments show that turn-level boundary supervision improves intervention localization, while reinforcement learning further improves the safety--utility trade-off. TurnGate outperforms existing guardrails and multi-turn monitoring baselines, and generalizes across risk domains, attacker pipelines, and target models. Our code is available at https://github.com/Graph-COM/TurnGate.

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