Objective and Impact Statement: Accurate organ segmentation is critical for many clinical applications at different clinical sites, which may have their specific application requirements that concern different organs. Introduction: However, learning high-quality, site-specific organ segmentation models is challenging as it often needs on-site curation of a large number of annotated images. Security concerns further complicate the matter. Methods: The paper aims to tackle these challenges via a two-phase aggregation-then-adaptation approach. The first phase of federated aggregation learns a single multi-organ segmentation model by leveraging the strength of 'bigger data', which are formed by (i) aggregating together datasets from multiple sites that with different organ labels to provide partial supervision, and (ii) conducting partially supervised learning without data breach. The second phase of site adaptation is to transfer the federated multi-organ segmentation model to site-specific organ segmentation models, one model per site, in order to further improve the performance of each site's organ segmentation task. Furthermore, improved marginal loss and exclusion loss functions are used to avoid 'knowledge conflict' problem in a partially supervision mechanism. Results and Conclusion: Extensive experiments on five organ segmentation datasets demonstrate the effectiveness of our multi-site approach, significantly outperforming the site-per-se learned models and achieving the performance comparable to the centrally learned models.