Medical images span a wide range of imaging protocols and anatomical regions, exhibiting two fundamental properties: inter-organ diversity–where different organs exhibit distinct structural patterns (e.g., hand vs. chest)–and intra-organ consistency–where each organ retains a coherent structure with subtle variations across patient (e.g., left vs. right hand). While existing foundation models typically focus on a single organ or combine organs across heterogeneous modalities–often failing to jointly capture both properties–we envision that a model purposefully built on these fundamental properties would yield representations with greater generalizability, robustness, and interpretability. To this end, we introduce a general-purpose and scalable framework for learning foundation models from diverse organs within a given imaging modality. We call our framework Coda, as it is explicitly designed to jointly capture both the consistency and diversity of anatomical structures, encoding high-level semantic relationships across distinct organs and fine-grained anatomical details within each organ. Our experiments in zero-shot, few-shot transfer, and full-transfer settings show that Coda, pretrained on 23 diverse organs, learns semantically rich representations that not only yield strong inter-organ and intra-organ discrimination capabilities but also offer superior generalizability and robustness on diverse tasks.