Scholarly publishing has been criticized for decades because of its commercialization and its exclusionary design. The problem is even deeper: scholarly publishing as it is designed today is unable to address major scientific emergencies, as the COVID pandemic demonstrated, as publishers were pressured to suspend licenses to access backfiles and many researchers and practitioners used preprints to communicate their ongoing findings. These ad hoc actions do not address other global emergencies (such as climate change and the loss of biodiversity) and it is morally indefensible to adopt them for some diseases and not others. In addition, scholarly publishing has developed into a system of research evaluation and career advancement, introducing distortions that do not benefit the equitable advancement of knowledge, while its high cost (and prices) trigger inequities that affect the most disadvantaged communities and individuals. There is vast experimentation, however, and there will be new models that we cannot even conceive of. It is impossible to be prescriptive about what each of these new or emerging models can do to address the current failings, but some principles can be identified. We are proposing a four-part test that can help decide which models to support, with the goal of starting a debate on what are the appropriate principles that should be adopted.