Development of neural circuitry depends on the integration of signaling pathways to coordinate specification, proliferation and differentiation of cell types in the right number, in the right place, at the right time. Zinc finger protein 423 (Zfp423), a 30-zinc finger transcription factor, forms alternate complexes with components of several developmental signaling pathways, suggesting it as a point of signal integration during brain development. We previously showed that mice lacking Zfp423 have reduced proliferation of cerebellar precursor cells, resulting in complete loss of vermis and variable hypoplasia of cerebellar hemispheres. Here, we show that Zfp423(-/-) hemisphere malformations are shaped by both genetic and non-genetic factors, producing distinct phenotype distributions in different inbred genetic backgrounds. In genetic mapping studies, we identify four additive modifier loci (Amzn1-4) and seven synthetically interacting loci (Smzn1.1-3.1) that together explain approximately one-third of the phenotypic variance. Strain-specific sequence polymorphism and expression data provide a reduced list of functional variant candidate genes at each modifier locus. Environmental covariates add only modest explanatory power, suggesting an additional stochastic component. These results provide a comprehensive analysis of sources of phenotype variation in a model of hindbrain malformation.