In the Watchman Route Problem (WRP), the task is to find a path for a watchman agent such that all locations in the given map will be visually seen by the watchman at least once during the path traversal. Recently, the problem has been optimally solved on a grid map using heuristic search. In this paper, we extend this work to the case of multiple agents. We call this problem the Multiple Watchman Route Problem (MWRP). In MWRP, the task is to find a path for each watchman such that each location on the map will be seen by at least one watchman. We optimally solve MWRP with heuristic search for two different objective functions with a number of A*-based variants, including an enhanced branching mechanism. We then provide an experimental study on these methods and on other attributes of this problem.