Multi-agent reinforcement learning (MARL) often relies on \emph{parameter sharing (PS)} to scale efficiently. However, purely shared policies can stifle each agent's unique specialization, reducing overall performance in heterogeneous environments. We propose \textbf{Low-Rank Agent-Specific Adaptation (LoRASA)}, a novel approach that treats each agent's policy as a specialized ``task'' fine-tuned from a shared backbone. Drawing inspiration from parameter-efficient transfer methods, LoRASA appends small, low-rank adaptation matrices to each layer of the shared policy, naturally inducing \emph{parameter-space sparsity} that promotes both specialization and scalability. We evaluate LoRASA on challenging benchmarks including the StarCraft Multi-Agent Challenge (SMAC) and Multi-Agent MuJoCo (MAMuJoCo), implementing it atop widely used algorithms such as MAPPO and A2PO. Across diverse tasks, LoRASA matches or outperforms existing baselines \emph{while reducing memory and computational overhead}. Ablation studies on adapter rank, placement, and timing validate the method's flexibility and efficiency. Our results suggest LoRASA's potential to establish a new norm for MARL policy parameterization: combining a shared foundation for coordination with low-rank agent-specific refinements for individual specialization.