Object-centric processes follow a paradigm in which a single process instance does not operate in isolation but interacts with other instances of the same or different processes. Recently, these processes have become increasingly popular in both academia and industry due to their relevance in various application scenarios. Predictive process monitoring is naturally still relevant for object-centric processes to predict the final outcome of individual process executions. A substantial body of research work exists to tackle the predictive monitoring task for object-centric processes. However, while object-centric processes already consider the interactions among objects, there may still be interferences among executions that are not explicitly represented through shared objects. Existing techniques for predictive monitoring for object-centric processes only consider the explicit object interactions, overlooking the hidden interferences. If these interferences have a significant influence on predicted KPIs of interest, the prediction accuracy is negatively impacted. This paper puts forward a technique that performs global predictions of all ongoing process executions together. Experiments on multiple processes show that indeed these global predictions are significantly more accurate, compared to the setting in which process executions are predicted in isolation by only considering the explicit interactions.