This study proposes a structured constructs model (SCM) to examine measurement in the context of a multidimensional learning progression (LP). The LP is assumed to have features that go beyond a typical multidimentional IRT model, in that there are hypothesized to be certain cross-dimensional linkages that correspond to requirements between the levels of the different dimensions. The new model builds on multidimensional item response theory models and change-point analysis to add cut-score and discontinuity parameters that embody these substantive requirements. This modeling strategy allows us to place the examinees in the appropriate LP level and simultaneously to model the hypothesized requirement relations. Results from a simulation study indicate that the proposed change-point SCM recovers the generating parameters well. When the hypothesized requirement relations are ignored, the model fit tends to become worse, and the model parameters appear to be more biased. Moreover, the proposed model can be used to find validity evidence to support or disprove initial theoretical hypothesized links in the LP through empirical data. We illustrate the technique with data from an assessment system designed to measure student progress in a middle-school statistics and modeling curriculum.