We introduce the Pose and Illumination agnostic Anomaly Detection (PIAD) problem, a generalization of pose-agnostic anomaly detection (PAD). Being illumination agnostic is critical, as it relaxes the assumption that training data for an object has to be acquired in the same light configuration of the query images that we want to test. Moreover, even if the object is placed within the same capture environment, being illumination agnostic implies that we can relax the assumption that the relative pose between environment light and query object has to match the one in the training data. We introduce a new dataset to study this problem, containing both synthetic and real-world examples, propose a new baseline for PIAD, and demonstrate how our baseline provides state-of-the-art results in both PAD and PIAD, not only in the new proposed dataset but also in existing datasets that were designed for the simpler PAD problem. Source code and data will be made publicly available upon paper acceptance.