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Does knowledge of language transfer spontaneously across language modalities? For example, do English speakers, who have had no command of a sign language, spontaneously project grammatical constraints from English to linguistic signs? Here, we address this question by examining the constraints on doubling. We first demonstrate that doubling (e.g., panana, generally, ABB) is amenable to two conflicting parses (identity vs. reduplication), depending on the level of analysis (phonology vs. morphology). We next show that speakers with no command of a sign language spontaneously project these two parses to novel ABB signs in American Sign language. Moreover, the chosen parse (for signs) is constrained by the morphology of spoken language. Hebrew speakers can project the morphological parse when doubling indicates diminution, but English speakers only do so when doubling indicates plurality, in line with the distinct morphological properties of their spoken languages. These observations suggest that doubling in speech and signs is constrained by a common set of linguistic principles that are algebraic, amodal and abstract.