Clinical notes are the backbone of electronic health records, often containing vital information not observed in other structured data. Unfortunately, the unstructured nature of clinical notes can lead to critical patient-related information being lost. Algorithms that organize clinical notes into distinct sections are often proposed in order to allow medical professionals to better access information in a given note. These algorithms, however, often assume a given partition over the note, and only classify section types given this information. In this paper, we propose a multi-task solution for note sectioning, where one model can identify context changes and label each section with its medically-relevant title. Results on in-distribution (MIMIC-III) and out-of-distribution (private held-out) datasets reveal that our multi-task approach can successfully identify note sections across different hospital systems.