Multi-agent cooperative motion planning offers the potential to improve safety and the overall traffic flow. However, many approaches for multi-agent driving do not incorporate traffic rules or do not generalize to arbitrary scenarios. To address these open problems, we propose a novel method to negotiate individual rule-compliant driving corridors and independently plan trajectories for each controlled agent in them. We incorporate predictions into the conflict negotiation process to enable decision-making over long time horizons. Our approach is applicable to arbitrary scenarios, including mixed cooperative and non-cooperative traffic participants, as demonstrated through our numerical experiments.