A framework with a data-driven model based approach to compute and analyze the operability sets is presented. The computationally expensive steady-state simulations are replaced by machine learning models developed through statistical analysis of selected rigorous simulations. The entire solution manifold is computed using a high-dimensional continuation algorithm. The framework is applied to a plant-wide system. The steps of the framework are discussed in depth within the context of the plant-wide system. The operability sets computed by high-dimensional continuation are analyzed in detail. Operability sets of lower dimensional subsystems are computed to gain better insights. Input behavior at cost optimal conditions and the multiplicities in the subsystems are also explored.