Multidimensionality and hierarchical data structure are common in assessment data. These design features, if not accounted for, can threaten the validity of the results and inferences generated from factor analysis, a method frequently employed to assess test dimensionality. In this article, we describe and demonstrate the application of the multilevel bifactor model to address these features in examining test dimensionality. The tool for this exposition is the Child Observation Record Advantage 1.5 (COR-Adv1.5), a child assessment instrument widely used in Head Start programs. Previous studies on this assessment tool reported highly correlated factors and did not account for the nesting of children in classrooms. Results from this study show how the flexibility of the multilevel bifactor model, together with useful model-based statistics, can be harnessed to judge the dimensionality of a test instrument and inform the interpretability of the associated factor scores.