The concept of a case describing all information relevant for one execution of a process is fundamental to process science. It is the conceptual lens through which process behavior is studied. The implicit assumption that cases partition behavior into distinct and separate executions hinders transferring established methods and techniques for process analysis and mining to object-centric settings. Here, processes operate over shared objects and hence behavior cannot easily be separated. To enable such a transfer, we need a suitable notion of object-centric case. This paper explores possible definitions for object-centric cases and executions grounded in object-centric event data. We propose formal definitions that generalize the classical setting. We specifically illustrate that, on one hand, any object-centric case notion has to break with the assumption of partitioning behavior, and on the other hand, this break enables new use cases. We conclude with a critical analysis of our proposal highlighting gaps and deficiencies that need to be addressed.