Cognitive capabilities can enhance a business process by offering automated analytics-based recommendations on key decisions by applying machine learning techniques. Yet the organizational adoption of such advanced capabilities is difficult as user acceptance of advice and recommendations from an automated system requires the development of trust over time. Business processes and the processes responsible for user engagement with enterprise cognitive systems need not only to be designed, but also have to change together with the supporting processes that can emerge and evolve over a period of time to monitor, evaluate, adjust, or modify the cognitively-enhanced business processes to enable employees to adapt to the enhanced capabilities of cognitive systems. In this paper, we propose a systematic modeling approach to study and guide the design and configuration of process architectures that help enterprises implement and evolve systems with cognitive capabilities. The use of suitable enterprise modeling techniques can facilitate the exploration and analysis of obstacles to adoption and guide the systematic search for viable modes of interaction and cooperation between a human user and a cognitive system.