The role of high-quality models is increasingly recognized for driving and documenting processes in safety-critical domains such as medical processes. In general, the environment of a complex process has to deal with multiple views referring to different concerns, agents, resources, locations, and so forth. The variety of needs along those views calls for multiple, complementary and consistent facets of a composite process model, where each facet addresses a specific view. Building multi-view process models is in our experience hard and error-prone. To address this challenge, the paper describes formal operators for composing process model facets in a coherent way and, conversely, for decomposing process models into specific facets that abstract from details irrelevant to a specific view. These operators are grounded on the formal trace semantics provided by our process language and its supporting analysis toolset. The paper shows how these operators are automated and reports on their use in a real case study of model construction for a particle-therapy center.