Legal Judgment Prediction (LJP) aims to predict the charge, relevant law article, and term of penalty from case descriptions. Existing LLM-as-Judge solutions apply retrieved historical cases to enhance prediction, but the retrieval might contain irrelevant and redundant information, thereby limiting their accuracy. Moreover, these solutions rely on a single LLM for prediction and lack mechanisms to address potential bias and hallucination in its inference. To address these limitations, we introduce the *Collaborative Reasoning with Reranked Multi-facet Retrieval* (**CoRe**) framework, which retrieves historical cases from multiple facets, reranks them as candidate precedents, and employs two collaborative LLM judges to make the final prediction. The two LLM judges are inspired by the collegiate bench mechanism in real-world judicial practices, where Judge A makes a preliminary prediction that guides Judge B in re-selecting precedents and producing the final prediction. Experiments on public datasets validate the effectiveness of our CoRe framework in terms of better prediction performance over the competitors.