Inbred genetic background significantly influences the expression of phenotypes associated with known genetic perturbations and can underlie variation in disease severity between individuals with the same mutation. However, the effect of epistatic interactions on the development of complex traits, such as craniofacial morphology, is poorly understood. Here, we investigated the effect of three inbred backgrounds (129X1/SvJ, C57BL/6J, and FVB/NJ) on the expression of craniofacial dysmorphology in mice (Mus musculus) with loss of function in three members of the Sprouty family of growth factor negative regulators (Spry1, Spry2, or Spry4) in order to explore the impact of epistatic interactions on skull morphology. We found that the interaction of inbred background and the Sprouty genotype explains as much craniofacial shape variation as the Sprouty genotype alone. The most severely affected genotypes display a relatively short and wide skull, a rounded cranial vault, and a more highly angled inferior profile. Our results suggest that the FVB background is more resilient to Sprouty loss of function than either C57 or 129, and that Spry4 loss is generally less severe than loss of Spry1 or Spry2 While the specific modifier genes responsible for these significant background effects remain unknown, our results highlight the value of intercrossing mice of multiple inbred backgrounds to identify the genes and developmental interactions that modulate the severity of craniofacial dysmorphology. Our quantitative results represent an important first step toward elucidating genetic interactions underlying variation in robustness to known genetic perturbations in mice.