This paper addresses the problem of predicting the occupancy of urban public transport vehicles with a network-wide framework where the effects of the interactions between multiple lines are jointly considered. In particular, we propose and compare several occupancy predictors, each of them differing in the amount of information used and in the prediction model adopted. We consider two prediction models: a behavioral model that assumes an explicit relation between some observed variables and the occupancy, and a machine learning model based on the LightGBM algorithm. We evaluate the proposed network-wide prediction framework on two real-world case studies related to the public transport network of the Swiss city of Zurich. The results show that predicting the occupancy for a target line while simultaneously considering the other lines in the network allows significant improvements in the accuracy of the predictions, especially in the corridors served by different interacting lines. The described methodology could be used by public transport agencies to improve the accuracy of the crowding information provided to passengers and to increase the attractiveness of public transport systems.