Coordinating a team of robots to reposition multiple objects in cluttered environments requires reasoning jointly about where robots should establish contact, how to manipulate objects once contact is made, and how to navigate safely and efficiently at scale. Prior approaches typically fall into two extremes -- either learning the entire task or relying on privileged information and hand-designed planners -- both of which struggle to handle diverse objects in long-horizon tasks. To address these challenges, we present a unified framework for collaborative multi-robot, multi-object non-prehensile manipulation that integrates flow-matching co-generation with anonymous multi-robot motion planning. Within this framework, a generative model co-generates contact formations and manipulation trajectories from visual observations, while a novel motion planner conveys robots at scale. Crucially, the same planner also supports coordination at the object level, assigning manipulated objects to larger target structures and thereby unifying robot- and object-level reasoning within a single algorithmic framework. Experiments in challenging simulated environments demonstrate that our approach outperforms baselines in both motion planning and manipulation tasks, highlighting the benefits of generative co-design and integrated planning for scaling collaborative manipulation to complex multi-agent, multi-object settings. Visit gco-paper.github.io for code and demonstrations.