The aim of this large-scale, preregistered, cross-linguistic study was to mediate between theories of the acquisition of inflectional morphology, which lie along a continuum from rule-based to analogy-based. Across three morphologically rich languages (Polish, Finnish and Estonian), 120 children (mean age 48.32 months, SD=7.0m) completed an experimental, elicited-production study of noun case marking. Confirmatory analyses found effects of surface-form (whole-word, token) frequency for Polish and Estonian, and phonological neighbourhood density (PND) for all three languages (using either our preregistered class-based or an exploratory form-based measure). An exploratory all-languages analysis yielded both main effects, and a predicted interaction, such that the effect of PND was greater for forms with lower surface-form frequency, which are less available for direct retrieval from memory. Cross-linguistic differences were investigated with exploratory analyses of case variance, affix syncretism and stem changes. We conclude that these findings are difficult to reconcile with accounts that posit rules or linguistic abstractions and are most naturally explained by analogy-based connectionist or exemplar accounts.