Machine Reading Comprehension (MRC) for question answering (QA), which aims to answer a question given the relevant context passages, is an important way to test the ability of intelligence systems to understand human language. Multiple-Choice QA (MCQA) is one of the most difficult tasks in MRC because it often requires more advanced reading comprehension skills such as logical reasoning, summarization, and arithmetic operations, compared to the extractive counterpart where answers are usually spans of text within given passages. Moreover, most existing MCQA datasets are small in size, making the learning task even harder. We introduce MMM, a Multi-stage Multi-task learning framework for Multi-choice reading comprehension. Our method involves two sequential stages: coarse-tuning stage using out-of-domain datasets and multi-task learning stage using a larger in-domain dataset to help model generalize better with limited data. Furthermore, we propose a novel multi-step attention network (MAN) as the top-level classifier for this task. We demonstrate MMM significantly advances the state-of-the-art on four representative MCQA datasets.