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Despite notable advancements in automatic speech recognition (ASR), performance tends to degrade when faced with adverse conditions. Generative error correction (GER) leverages the exceptional text comprehension capabilities of large language models (LLM), delivering impressive performance in ASR error correction, where N-best hypotheses provide valuable information for transcription prediction. However, GER encounters challenges such as fixed N-best hypotheses, insufficient utilization of acoustic information, and limited specificity to multi-accent scenarios. In this paper, we explore the application of GER in multi-accent scenarios. Accents represent deviations from standard pronunciation norms, and the multi-task learning framework for simultaneous ASR and accent recognition (AR) has effectively addressed the multi-accent scenarios, making it a prominent solution. In this work, we propose a unified ASR-AR GER model, named MMGER, leveraging multi-modal correction, and multi-granularity correction. Multi-task ASR-AR learning is employed to provide dynamic 1-best hypotheses and accent embeddings. Multi-modal correction accomplishes fine-grained frame-level correction by force-aligning the acoustic features of speech with the corresponding character-level 1-best hypothesis sequence. Multi-granularity correction supplements the global linguistic information by incorporating regular 1-best hypotheses atop fine-grained multi-modal correction to achieve coarse-grained utterance-level correction. MMGER effectively mitigates the limitations of GER and tailors LLM-based ASR error correction for the multi-accent scenarios. Experiments conducted on the multi-accent Mandarin KeSpeech dataset demonstrate the efficacy of MMGER, achieving a 26.72% relative improvement in AR accuracy and a 27.55% relative reduction in ASR character error rate, compared to a well-established standard baseline.