Low-Rank Adaptation (LoRA) for large language models (LLMs) has achieved significant success in various domains. So far, most algorithms in the LoRA-family rely on global low-rank factors spanning the entire update weight matrix (𝛥 𝐖). Through careful analysis, however, we observe that the 𝛥 𝐖 during fine-tuning typically exhibit heterogeneous subspace clusters, each corresponding to specific sub-sets of rows and columns. This structural heterogeneity suggests that global low-rank factors may not optimally capture the local variations needed for effective model adaptation. To address this limitation, we propose LoRA within Clustered Parameter Subspaces, or CPS-LoRA, which performs independent low-rank updates within clustered blocks of parameter matrices. The key idea is to group the rows/columns of the update matrix into locally coherent, and maximally uncorrelated subspaces, perform low-rank adaptations in each subspace, and iteratively update the partition and local adaptations. This allows adapting to local structures more precisely while preserving high efficiency. Theoretical analysis reveals that in case 𝛥 𝐖 can be partitioned into subspace blocks with non-overlapping basis, CPS-LoRA have superior parameter efficiency than global adaptations. Empirical evaluations further demonstrate better rank utilization of CPS-LoRA and its consistent improvements against LoRA (and variants) by up to 3.0% in absolute accuracy in various benchmarks.