A configurable process model captures a family of related process models in a single artifact. Such models are intended to be configured to fit the requirements of specific organizations or projects, leading to individualized process models that are subsequently used for domain analysis or solution design. This article proposes a formal foundation for individualizing configurable process models incrementally, while preserving correctness, both with respect to syntax and behavioral semantics. Specifically, assuming the configurable process model is behaviorally sound, the individualized process models are guaranteed to be sound. The theory is first developed in the context of Petri nets and then extended to a process modeling notation widely used in practice, namely Event-driven Process Chains.