Process mining on business process execution data has focused primarily on orchestration-type processes performed in a single organization (intra-organizational). Collaborative (inter-organizational) processes, unlike those of orchestration type, expand several organizations (for example, in e-Government), adding complexity and various challenges both for their implementation and for their discovery, prediction, and analysis of their execution. Predictive process monitoring is based on exploiting execution data from past instances to predict the execution of current cases. It is possible to make predictions on the next activity and remaining time, among others, to anticipate possible deviations, violations, and delays in the processes to take preventive measures (e.g., re-allocation of resources). In this work, we propose an extension for collaborative processes of traditional process prediction, considering particularities of this type of process, which add information of interest in this context, for example, the next activity of which participant or the following message to be exchanged between two participants.