Processes are a key application area for formal models of concurrency. The core concepts of Petri nets have been adopted in research and industrial practice to describe and analyze the behavior of processes where each instance is executed in isolation. Unaddressed challenges arise when instances of processes may interact with each other in a one-to-many or many-to-many fashion. So far, behavioral models for describing such behavior either also include an explicit data model of the processes to describe many-to-many interactions, or cannot provide precise operational semantics. In this paper, we study the problem in detail through a fundamental example and evolve a few existing concepts from net theory towards many-to-many interactions. Specifically, we show that three concepts are required to provide an operational, true concurrency semantics to describe the behavior of processes with many-to-many interactions: unbounded dynamic synchronization of transitions, cardinality constraints limiting the size of the synchronization, and history-based correlation of token identities. The resulting formal model is orthogonal to all existing data modeling techniques, and thus allows to study the behavior of such processes in isolation, and to combine the model with existing and future data modeling techniques.