AbstractThe linearization of unboundedly many syntactic structures given a finite number of ordering instructions poses a compositionality problem similar to the semantic problem of determining the meanings of unboundedly many structures. We discuss this challenge and use various constructions such as Right‐Node Raising that have been argued to involve multidominance—and that combine a remarkable productivity across and inside languages with a sensitivity to linear order—to tease apart different theories of linearization. We use data from such constructions, including new data provided in the paper, to argue in favor of a specific view of linearization first proposed in Bachrach & Katzir, one in which linearization compatibility requirements are computed very locally, at every node in the structure.