Abstract. We propose an integrated framework of Collaborating Humans and AIs (CHA) for the design, analysis, and critique of human-AI applications in current and future workplaces. Through four use cases, we explore different configurations of humans working with intelligent systems, informed by a 70-year history of frameworks of human-machine interaction. We make two primary contributions: (1) In contrast to prior analyses of mixed-initiative human-AI systems, we demonstrate that complex organizational applications involve dynamic shifts and exchanges of human and machine initiative. (2) We extend the analyses to include multi-user configurations, in which we can examine the sometimes-invisible human roles behind those structures, interrogate power relationships, and uncover mismatches between the desired and available levels of human and AI initiative.