In robotics, coordinating a group of robots is an essential task. This work presents the communication-constrained multi-agent multi-goal path planning problem and proposes a graph-search based algorithm to address this task. Given a fleet of robots, an environment represented by a weighted graph, and a sequence of goals, the aim is to visit all the goals without breaking the communication constraints between the agents, minimizing the completion time. The resulting paths produced by our approach show how the agents can coordinate their individual paths, not only with respect to the next goal but also with respect to all future goals, all the time keeping the communication within the fleet intact.