The ideal of scientific progress is that we accumulate measurements and integrate these into theory, but recent discussion of replicability issues has cast doubt on whether psychological research conforms to this model. Developmental research – especially with infant participants – also has discipline-specific replicability challenges, including small samples due to high recruitment costs and limited measurement methods. Inspired by collaborative replication efforts in cognitive and social psychology, we describe a proposal for assessing and promoting replicability in infancy research: large-scale, multi-lab replication efforts aiming for a more precise understanding of key developmental phenomena. The ManyBabies project, our instantiation of this proposal, will not only help us estimate how robust and replicable these phenomena are, but also gain new theoretical insights into how they vary across ages, linguistic communities, and measurement methods. This project has the potential for a variety of positive outcomes, including less-biased estimates of theoretically-important effects, estimates of variability that can be used for later study planning, and a series of best-practices blueprints for future infancy research.