Accurate segmentation of cell nuclei in histopathology images is essential for numerous biomedical research and clinical applications. However, existing cell nucleus segmentation methods only consider a single dataset (i.e., primary domain), while neglecting to leverage supplementary data from diverse sources (i.e., auxiliary domains) to reduce overfitting and enhance the performance. Although incorporating multiple datasets could alleviate overfitting, it often exacerbates performance drops caused by domain shifts. In this work, we introduce Adversarial Multi-domain Alignment of Segment Anything Model (AMA-SAM) that extends the Segment Anything Model (SAM) to overcome these obstacles through two key innovations. First, we propose a Conditional Gradient Reversal Layer (CGRL), a multi-domain alignment module that harmonizes features from diverse domains to promote domain-invariant representation learning while preserving crucial discriminative features for the primary dataset. Second, we address SAM's inherent low-resolution output by designing a High-Resolution Decoder (HR-Decoder), which directly produces fine-grained segmentation maps in order to capture intricate nuclei boundaries in high-resolution histology images. To the best of our knowledge, this is the first attempt to adapt SAM for multi-dataset learning with application to histology nuclei segmentation. We validate our method on several publicly available datasets, demonstrating consistent and significant improvements over state-of-the-art approaches.