An important class of techniques for resonant anomaly detection in high energy physics builds models that can distinguish between reference and target datasets, where only the latter has appreciable signal. Such techniques, including Classification Without Labels (CWoLa) and Simulation Assisted Likelihood-free Anomaly Detection (SALAD) rely on a single reference dataset. They cannot take advantage of commonly-available multiple datasets and thus cannot fully exploit available information. In this work, we propose generalizations of CWoLa and SALAD for settings where multiple reference datasets are available, building on weak supervision techniques. We demonstrate improved performance in a number of settings with real and synthetic data. As an added benefit, our generalizations enable us to provide finite-sample guarantees, improving on existing asymptotic analyses.