Pharmacovigilance currently faces several unsolved challenges. Of particular importance are issues concerning how to ascertain, collect, confirm, and communicate the best evidence to assist the clinical choice for individual patients. Here, we propose that these practical challenges partially stem from deeper fundamental issues concerning the epistemology of pharmacovigilance. After reviewing some of the persistent challenges, recent measures, and suggestions in the current pharmacovigilance literature, we support the argument that the detection of potential adverse drug reactions ought to be seen as a serendipitous scientific discovery. We further take up recent innovations from the multidisciplinary field of serendipity research about the importance of networks, diversity of expertise, and plurality of methodological perspectives for cultivating serendipitous discovery. Following this discussion, we explore how pharmacovigilance could be systematized in a way that optimizes serendipitous discoveries of untargeted drug effects, emerging from the clinical application. Specifically, we argue for the promotion of a trans-disciplinary responsive network of scientists and stakeholders. Trans-disciplinarity includes extending the involvement of stakeholders beyond the regulatory community, integrating diverse methods and sources of evidence, and enhancing the ability of diverse groups to raise signals of harms that ought to be followed up by the network. Consequently, promoting a trans-disciplinary approach to pharmacovigilance is a long-term effort that requires structural changes in medical education, research, and enterprise. We suggest a number of such changes, discuss to what extent they are already in process, and indicate the advantages from both epistemological and ethical perspectives.