While there is a widespread belief that artificial general intelligence—or even superhuman AI—is imminent, complex problems in expert domains are far from being solved. We argue that such problems require human–AI cooperation and that the current state of the art in generative AI is unable to play the role of a reliable partner due to a multitude of shortcomings, including difficulty in keeping track of a complex solution artifact (e.g., a software program), limited support for versatile human preference expression, and lack of adapting to human preference in an interactive setting. To address these challenges, we propose HAI-Co2, a novel human–AI co-construction framework. We take first steps towards a formalization of HAI-Co2 and discuss the difficult open research problems that it faces.