In acoustic and bioelectrical environments characterized by multiple simultaneous sources, effective blind source separation from sensor response mixtures becomes difficult as the number of sources increases—especially when the true number of sources is both unknown and changing over time. However, in some environments, non-sensor information can provide useful hypotheses for some sources. Focusing for convenience on the acoustic case, we propose an adaptive filtering architecture for validating such hypotheses, extracting an acoustic representation of valid hypotheses, and improving the separation of the remaining “hidden” acoustic sources. We evaluate the performance of this “Only Mostly Blind Source Separation” algorithm on synthesized instantaneous (bioelectrical-like), synthesized non-instantaneous, and true convolutive acoustic mixtures of simultaneous speech material.