This paper presents a framework for multi-agent navigation in structured but dynamic environments, integrating three key components: a shared semantic map encoding metric and semantic environmental knowledge, a claim policy for coordinating access to areas within the environment, and a Model Predictive Controller for generating motion trajectories that respect environmental and coordination constraints. The main advantages of this approach include: (i) enforcing area occupancy constraints derived from specific task requirements; (ii) enhancing computational scalability by eliminating the need for collision avoidance constraints between robotic agents; and (iii) the ability to anticipate and avoid deadlocks between agents. The paper includes both simulations and physical experiments demonstrating the framework's effectiveness in various representative scenarios.