Large language models (LLMs) based Multilingual Knowledge Graph Completion (MKGC) aim to predict missing facts by leveraging LLMs' multilingual understanding capabilities, improving the completeness of multilingual knowledge graphs (KGs). However, existing MKGC research underutilizes the multilingual capabilities of LLMs and ignores the shareability of cross-lingual knowledge. In this paper, we propose a novel MKGC framework that leverages multilingual shared knowledge to significantly enhance performance through two components: Knowledge-level Grouped Mixture of Experts (KL-GMoE) and Iterative Entity Reranking (IER). KL-GMoE efficiently models shared knowledge, while IER significantly enhances its utilization. To evaluate our framework, we constructed a mKG dataset containing 5 languages and conducted comprehensive comparative experiments with existing state-of-the-art (SOTA) MKGC method. The experimental results demonstrate that our framework achieves improvements of 5.47\%, 3.27\%, and 1.01\% in the Hits@1, Hits@3, and Hits@10 metrics, respectively, compared with SOTA MKGC method. Further experimental analysis revealed the properties of knowledge sharing in settings of unseen and unbalanced languages. We have released the dataset and code for our work on https://anonymous.4open.science/r/KL-GMoE-A8E4.