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The Segment Anything Model (SAM) represents a significant breakthrough into foundation models for computer vision, providing a large-scale image segmentation model. However, despite SAM's zero-shot performance, its segmentation masks lack fine-grained details, particularly in accurately delineating object boundaries. Therefore, it is both interesting and valuable to explore whether SAM can be improved towards highly accurate object segmentation, which is known as the dichotomous image segmentation (DIS) task. To address this issue, we propose DIS-SAM, which advances SAM towards DIS with extremely accurate details. DIS-SAM is a framework specifically tailored for highly accurate segmentation, maintaining SAM's promptable design. DIS-SAM employs a two-stage approach, integrating SAM with a modified advanced network that was previously designed to handle the prompt-free DIS task. To better train DIS-SAM, we employ a ground truth enrichment strategy by modifying original mask annotations. Despite its simplicity, DIS-SAM significantly advances the SAM, HQ-SAM, and Pi-SAM ~by 8.5%, ~6.9%, and ~3.7% maximum F-measure