Sharing sensitive texts for scientific purposes requires appropriate techniques to protect the privacy of patients and healthcare personnel. Anonymizing textual data is particularly challenging due to the presence of diverse unstructured direct and indirect identifiers. To mitigate the risk of re-identification, this work introduces a schema of nine categories of indirect identifiers designed to account for different potential adversaries, including acquaintances, family members and medical staff. Using this schema, we annotate 100 MIMIC-III discharge summaries and propose baseline models for identifying indirect identifiers. We will release the annotation guidelines, annotation spans (6,199 annotations in total) and the corresponding MIMIC-III document IDs to support further research in this area.