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Mobility-as-a-service systems are becoming increasingly important in the context of smart cities, with challenges arising for public agencies to obtain data from private operators. Only limited mobility data are typically provided to city agencies, which are not enough to support their decision-making. This study proposed an entropy-maximizing gravity model to predict origin–destination patterns of both passenger and mobility fleets with only partial operator data. An iterative balancing algorithm was proposed to efficiently reach the entropy maximization state. With different trip length distributions data available, two calibration applications were discussed and validated with a small-scale numerical example. Tests were also conducted to verify the applicability of the proposed model and algorithm to large-scale real data from Chicago transportation network companies. Both shared-ride and single-ride trips were forecast based on the calibrated model, and the prediction of single-ride has a higher level of accuracy. The proposed solution and calibration algorithms are also efficient to handle large scenarios. Additional analyses were conducted for north and south sub-areas of Chicago and revealed different travel patterns in these two sub-areas.