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Object region mining is a critical step for weakly-supervised semantic segmentation. Most recent methods mine the object regions by expanding the seed regions localized by class activation maps. They generally do not consider the sizes of objects and apply a monotonous procedure to mining all the object regions. Thus their mined regions are often insufficient in number and scale for large objects, and on the other hand easily contaminated by surrounding backgrounds for small objects. In this paper, we propose a novel multi-miner framework to perform a region mining process that adapts to diverse object sizes and is thus able to mine more integral and finer object regions. Specifically, our multi-miner leverages a parallel modulator to check whether there are remaining object regions for each single object, and guide a category-aware generator to mine the regions of each object independently. In this way, the multi-miner adaptively takes more steps for large objects and fewer steps for small objects. Experiment results demonstrate that the multi-miner offers better region mining results and helps achieve better segmentation performance than state-of-the-art weakly-supervised semantic segmentation methods.