This paper proposes a method that leverages constraints on the entire team, rather than individual agents, to address safety issues in multi-agent reinforcement learning. Existing safe reinforcement learning algorithms constrain agent behavior to limit exploration, which is crucial for discovering effective cooperative behaviors. In this paper, we present Entropy Search (E2C), a method for constrained multi-agent reinforcement learning. E2C encourages exploration by maximizing observation entropy, facilitating the learning of safe and effective cooperative behaviors. Extensive experimental results demonstrate that E2C performs equally or better than existing unconstrained and constrained baseline models, reducing unsafe behaviors by up to 50%.