Vehicle-to-anything connectivity, especially for autonomous vehicles, promises to increase passenger comfort and safety of road traffic, for example, by sharing perception and driving intention. Cooperative maneuver planning uses connectivity to enhance traffic efficiency, which has, so far, been mainly considered for automated intersection management. In this article, we present a novel cooperative maneuver planning approach that is generalized to various situations found in urban traffic. Our framework handles challenging mixed traffic, that is, traffic comprising both cooperative connected vehicles and other vehicles at any distribution. Our solution is based on an optimization approach accompanied by an efficient heuristic method for high-load scenarios. We extensively evaluate the proposed planer in a distinctly realistic simulation framework and show significant efficiency gains already at a cooperation rate of 40%. Traffic throughput increases, while the average waiting time and the number of stopped vehicles are reduced, without impacting traffic safety.