End-to-end multilingual ASR aims to transcribe speech from different languages into corresponding text, but is often limited by scarce multilingual data. LLM-based ASR aligns speech encoder outputs with LLM input space via a projector and has achieved notable success. However, prior work mainly improves performance by increasing data, with little focus on cross-lingual knowledge sharing. Moreover, a single complex projector struggles to capture both shared and language-specific features effectively. In this work, we propose MOSA (Mixture of Simple Adapters), leveraging a Mixture-of-Experts mechanism to combine lightweight adapters that learn shared and language-specific knowledge. This enables better utilization of high-resource language data to support low-resource languages, mitigating data scarcity issues. Experimental results show that MOSA-Base achieves a 15.4\% relative reduction in average WER compared to the Baseline-Base and consistently outperforms it across all languages. Remarkably, MOSA-Base surpasses the Baseline-Base even when trained with only 60\% of its parameters. Similarly, MOSA-Large outperforms the Baseline-Large in average WER and demonstrates greater robustness to data imbalance. Ablation studies further indicate that MOSA is more effective at handling individual languages and learning both language-specific and shared linguistic knowledge. These findings support that, in LLM-based ASR, a mixture of simple adapters is more effective than a single, complex adapter design.