In recent years, there has been a growing interest in exploring dialogues with more complex goals, such as negotiation, persuasion, and emotional support, which go beyond traditional service-focused dialogue systems. Apart from the requirement for much more sophisticated strategic reasoning and communication skills, a significant challenge of these tasks lies in the difficulty of objectively measuring the achievement of their goals in a quantifiable way, making it difficult for existing research to directly optimize the dialogue procedure towards them. In our work, we emphasize the multifaceted nature of complex dialogue goals and argue that it is more feasible to accomplish them by comprehensively considering and jointly promoting their different aspects. To this end, we propose a novel dialogue framework, Cooper, which coordinates multiple specialized agents, each dedicated to a specific dialogue goal aspect separately, to approach the complex objective. Through this divide-and-conquer manner, we make complex dialogue goals more approachable and elicit greater intelligence via the collaboration of individual agents. Experiments on persuasion and emotional support dialogues demonstrate the superiority of our method over a set of competitive baselines. Our codes are available at https://github.com/YiCheng98/Cooper.