In this paper, we tackle the task of category-agnostic pose estimation (CAPE), which aims to predict poses for objects of any category with few annotated samples. Previous works either rely on local matching between features of support and query samples or require support keypoint identifier. The former is prone to overfitting due to its sensitivity to sparse samples, while the latter is impractical for the open-world nature of the task. To overcome these limitations, we propose ESCAPE - a Bayesian framework that learns a prior over the features of keypoints. The prior can be expressed as a mixture of super-keypoints, each being a high-level abstract keypoint that captures the statistics of semantically related keypoints from different categories. We estimate the super-keypoints from base categories and use them in adaptation to novel categories. The adaptation to an unseen category involves two steps: first, we match each novel keypoint to a related super-keypoint; and second, we transfer the knowledge encoded in the matched super-keypoints to the novel keypoints. For the first step, we propose a learnable matching network to capture the relationship between the novel keypoints and the super-keypoints, resulting in a more reliable matching. ESCAPE mitigates overfitting by directly transferring learned knowledge to novel categories while it does not use keypoint identifiers.