Business process monitoring approaches have thus far mainly focused on monitoring the execution of a process with respect to a single process model. However, in some cases it is necessary to consider multiple process specifications simultaneously. In addition, these specifications can be procedural, declarative, or a combination of both. For example, in the medical domain, a clinical guideline describing the treatment of a specific disease cannot account for all possible co-factors that can coexist for a specific patient and therefore additional constraints may need to be considered. In some cases, these constraints may be incompatible with clinical guidelines, therefore requiring the violation of either the guidelines or the constraints. In this paper, we propose a solution for monitoring the interplay of hybrid process specifications expressed as a combination of (data-aware) Petri nets and temporal logic rules. During the process execution, if these specifications are in conflict with each other, it is possible to violate some of them. The monitoring system is equipped with a violation cost model according to which the system can recommend the next course of actions in a way that would either avoid possible violations or minimize the total cost of violations.