The rapid advancement of Large Language Models (LLMs) has introduced significant challenges in moderating user-model interactions. While LLMs demonstrate remarkable capabilities, they remain vulnerable to adversarial attacks, particularly ``jailbreaking'' techniques that bypass content safety measures. Current content moderation systems, which primarily rely on input prompt filtering, have proven insufficient, with techniques like Best-of-N (BoN) jailbreaking achieving success rates of 80% or more against popular LLMs. In this paper, we introduce Flexible LLM-Assisted Moderation Engine (FLAME): a new approach that shifts the focus from input filtering to output moderation. Unlike traditional circuit-breaking methods that analyze user queries, FLAME evaluates model responses, offering several key advantages: (1) computational efficiency in both training and inference, (2) enhanced resistance to BoN jailbreaking attacks, and (3) flexibility in defining and updating safety criteria through customizable topic filtering. Our experiments demonstrate that FLAME significantly outperforms current moderation systems. For example, FLAME reduces attack success rate in GPT-4o-mini and DeepSeek-v3 by a factor of ~9, while maintaining low computational overhead. We provide comprehensive evaluation on various LLMs and analyze the engine's efficiency against the state-of-the-art jailbreaking. This work contributes to the development of more robust and adaptable content moderation systems for LLMs.