In a cross-organizational service-based process provisioning scenario, one provider is likely to execute a given business process to serve several customers. Each customer may hold different expectations about the way this process can be monitored. We present a solution allowing the provider to support the requirements of different customers on the monitoring of a given process, i.e., offering them the opportunity to customize the way a process will be monitored. We propose a multi-dimensional classification model of patterns for process monitoring and rules to compose the patterns to design customized monitoring infrastructures. The fit for purpose of the patterns is evaluated empirically, whereas the feasibility of our solution is demonstrated by a tool supporting process monitoring customization adhering to our pattern design and composition methodology.