Conservation actions are notoriously difficult to design and implement in contexts of value pluralism. These difficulties are compounded in the case of biological invasion mitigation. Biological invasions are major threats to biodiversity and ecosystems. Preventing or mitigating biological invasions accordingly plays a key role in conservation policies. The relationship between human beings and invasive species is, however, complex, not unequivocal, and presents a variety of moral aspects. The practical and ethical reasons used to champion actions targeting populations of invasive species are questioned both in the literature and by actors and stakeholders in the field. The resulting debates between advocates and critics of biological invasion mitigation are doomed to remain sterile unless the whole diversity of points of view is considered and the relationships between human beings and non-human beings (i.e., plants and animals) are considered in their full complexity. As conservation biologists involved in invasion research, we argue that, instead of bemoaning such difficulties, conservation biologists should see the challenge to face this diversity as an opportunity to innovate. We present a heuristic, based on theories of deliberative democracy and multispecies anthropology, to help consider this pluralism and this complexity when identifying management options. This heuristic consists of identifying the spectrum of points of view of human and non-human beings concerned and assessing how acceptable the various actions are to all these points of view, until a course of action acceptable to all is found (if possible). We argue that by elaborating management options, which are arguably acceptable to all, including to members of the targeted invasive populations themselves, we can design more robust conservation solutions. We show how such an approach can be implemented in practice without paralyzing biological invasion mitigation.