A foundational goal of linguistics is to investigate whether shared features of the human cognitive system can explain how linguistic patterns are distributed across languages. In this paper we report a series of artificial language learning experiments which aim to test a hypothesised link between cognition and a persistent regularity of morpheme order: number morphemes (e.g., plural markers) tend to be ordered closer to noun stems than case morphemes (e.g., accusative markers) (Universal 39; Greenberg, 1963). We argue that this typological tendency may be driven by learners’ bias towards orders that reflect scopal relationships in morphosyntactic and semantic composition (Bybee, 1985; Rice, 2000; Culbertson & Adger, 2014). This bias is borne out by our experimental results: learners—in the absence of any evidence on how to order number and case morphology—consistently produce number closer to the noun stem. We replicate this effect across two populations (English and Japanese speakers). We also find that it holds independent of morpheme position (prefixal or suffixal), degree of boundedness (free or bound morphology), frequency, and which particular case/number feature values are instantiated in the overt markers (accusative or nominative, plural or singulative). However, we show that this tendency can be reversed when the form of the case marker is made highly dependent on the noun stem, suggesting an influence of an additional bias for local dependencies. Our results provide evidence that universal features of cognition may play a causal role in shaping the relative order of morphemes.