Sequence recommendation (SeqRec) aims to predict the next item a user will interact with by understanding user intentions and leveraging collaborative filtering information. Large language models (LLMs) have shown great promise in recommendation tasks through prompt-based, fixed reflection libraries, and fine-tuning techniques. However, these methods face challenges, including lack of supervision, inability to optimize reflection sources, inflexibility to diverse user needs, and high computational costs. Despite promising results, current studies primarily focus on reflections of users' explicit preferences (e.g., item titles) while neglecting implicit preferences (e.g., brands) and collaborative filtering information. This oversight hinders the capture of preference shifts and dynamic user behaviors. Additionally, existing approaches lack mechanisms for reflection evaluation and iteration, often leading to suboptimal recommendations. To address these issues, we propose the Mixture of REflectors (MoRE) framework, designed to model and learn dynamic user preferences in SeqRec. Specifically, MoRE introduces three reflectors for generating LLM-based reflections on explicit preferences, implicit preferences, and collaborative signals. Each reflector incorporates a self-improving strategy, termed refining-and-iteration, to evaluate and iteratively update reflections. Furthermore, a meta-reflector employs a contextual bandit algorithm to select the most suitable expert and corresponding reflections for each user's recommendation, effectively capturing dynamic preferences. Extensive experiments on three real-world datasets demonstrate that MoRE consistently outperforms state-of-the-art methods, requiring less training time and GPU memory compared to other LLM-based approaches in SeqRec.