Knowledge graph completion (KGC) aims to infer missing triples from existing data. While tensor decomposition-based models offer strong expressiveness, their large core tensors often cause overfitting. We propose MuC, a multi-core tensor model that factorizes the core tensor into several smaller cores and introduces a core attention mechanism to dynamically select relevant cores based on entity-relation input. To encourage diversity among cores, we design a geometric consistency constraint, and to stabilize multi-path interactions, we generalize embedding norm regularization into channel regularization. Experiments show that MuC improves MRR by 22.83% on FB15k-237 and 21.51% on YAGO3-10 compared to strong baselines. Further analysis of core attention weights and dataset characteristics demonstrates the effectiveness of MuC’s dynamic core selection in enhancing adaptability and expressiveness.