The research focused on modelling the complexity of a complex social service system based on a novel heuristic derived from the system elements part count approach and the application of the Hybrid Structural Interaction Matrix (HSIM) methodology. A generic institution was modeled to create the heuristic and then applied to several case institutions. The dataset contains the identified elements for the generic institution, the matrices created through the application of the HSIM method, and the data used to calculate the complexity scores for each case.