While current federated multimodal continual learning over mixture-of-experts low-rank adaptation (MoE-LoRA) is built on the unverified assumption that routing isolates task-specific knowledge into disjoint experts, we argue that routing operates per-sample, while forgetting accumulates across the task sequence, and gradient conflict persists within each expert even when routing is maximally polarized. Moreover, activation-subspace protection can also fail because, under parameter-efficient fine-tuning, it entangles tasks due to a dimension-counting bound, and federated averaging (FedAvg) disrupts client-side orthogonality. To address this, we propose PRISM (Per-expert Routing-projection Interference-informed Subspace Method), which maintains a per-expert gradient subspace basis whose orthogonality is preserved under FedAvg and reinterprets MoE routing as a capacity allocator. Our results show that, on LLaVA-1.5-7B, LLaVA-1.5-13B, and Qwen2.5-VL-7B across CoIN-6 and CoIN-Long-10, PRISM outperforms sixteen the state of the art baselines in average accuracy. Compared to the best federated multimodal baseline, the performance margin increases from +3.23 pp on CoIN-6 to +6.06 pp on CoIN-Long-10.

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