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OAR segmentation is a critical step in radiotherapy of head and neck (H&N) cancer, where inconsistencies across radiation oncologists and prohibitive labor costs motivate automated approaches. However, leading methods using standard fully convolutional network workflows that are challenged when the number of OARs becomes large, e.g. > 40. For such scenarios, insights can be gained from the stratification approaches seen in manual clinical OAR delineation. This is the goal of our work, where we introduce stratified organ at risk segmentation (SOARS), an approach that stratifies OARs into anchor, mid-level, and small & hard (S&H) categories. SOARS stratifies across two dimensions. The first dimension is that distinct processing pipelines are used for each OAR category. In particular, inspired by clinical practices, anchor OARs are used to guide the mid-level and S&H categories. The second dimension is that distinct network architectures are used to manage the significant contrast, size, and anatomy variations between different OARs. We use differentiable neural architecture search (NAS), allowing the network to choose among 2D, 3D or Pseudo-3D convolutions. Extensive 4-fold cross-validation on 142 H&N cancer patients with 42 manually labeled OARs, the most comprehensive OAR dataset to date, demonstrates that both pipeline- and NAS-stratification significantly improves quantitative performance over the state-of-the-art (from 69.52% to 73.68% in absolute Dice scores). Thus, SOARS provides a powerful and principled means to manage the highly complex segmentation space of OARs.