Continual multimodal instruction tuning requires multimodal large language models to acquire new task abilities sequentially while preserving previously learned knowledge. LoRA-MoE provides a promising solution by introducing expert-based capacity, but repeatedly learning and maintaining full LoRA experts leads to substantial parameter overhead. This raises a natural question: is full expert expansion necessary for every new task? To answer it, we analyze the SVD of task-specific LoRA updates and observe substantial overlap in their input- and output-side LoRA direction subspaces, with task-specific adaptation largely captured by lightweight coordinates over these subspaces. Motivated by this observation, we propose CoRe-MoE, a Compact Reusable MoE framework for parameter-efficient continual multimodal instruction tuning. CoRe-MoE extracts reusable input- and output-side direction bases from an initial expert bank, and for subsequent tasks trains only compact coordinate experts together with task-specific low-rank routers. Experiments on two representative MLLMs show that CoRe-MoE improves final average performance over the strongest competing baseline by up to 5.90 points, while using less than 1% of the trainable parameters required by sequential LoRA for later tasks. The code is publicly available at https://github.com/runzezz/CoRe-MoE.

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