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Despite the widespread adoption of process management systems (PrMS) by industry, there exist numerous processes that cannot be adequately supported by PrMS so far. A common characteristic of these processes, which is usually neglected by traditional activity-centric PrMS, is the role of data as driver for process modeling and enactment. To overcome the limitations caused by missing integration of data and process, several data-centric process management approaches have emerged. A popular one is the Case Handling (CH) paradigm. However, previous case studies pointed out that, although it targets some of the limitations from activity-centric PrMS, the integration of processes and data supported by CH is still unsatisfactory. In this paper, we present the lessons learned from previous case studies and discuss the limitations of CH. We then present the PHILharmonicFlows framework, which enhances the power of data-centric approaches such as CH by enforcing a well-defined modeling methodology governing the object-centric specification and execution of processes and based on a formal operational semantics.