Recent work suggests new modes of human-AI collaboration are emerging, particularly in the exploration of new AI tools within specialized domains. We develop a theoretical basis for understanding these emergent modes using concepts from the field of design, integrating Herbert Simon’s Science of Design with the broader design field that builds upon and expands Donald Schön’s reflective design tradition. We build a classificatory scheme of design cognitions and processes, validating these concepts through a set of engineering design (AI) studies, ultimately contributing to a more comprehensive model of human-AI interaction. By contrasting Simon's modular approach with the broader design approach (as based on Schön’s reflective and process-oriented view), we highlight the dynamic role of human cognitions—particularly, reframing and sensemaking—when co-designing with AI, while also emphasizing domain expertise. The iterative nature of the engagement process is fundamentally tied to designers bringing their knowledge, framing and sensemaking to bear on the AI’s responses. This design perspective helps capture richer human manners of expressing knowledge while working with AI. It shows that the study of human-AI interactions may need to account for human capabilities beyond what is assumed of modular augmentation approaches. This effort also contributes to the call for studies of design in management.