We consider a dynamic model of sender-receiver stopping games with multiple senders and only one receiver. The state of the world follows an iid--process throughout the game. At each period, each sender observes the current state and sends a message to the receiver, suggesting either to stop or to continue. The receiver, only seeing the collections of messages but not the state, decides either to stop the game, or to continue which takes the game to the next period. The payoff to each player is a function of the state when the receiver quits, with higher states leading to better payoffs, and it can be discounted or undiscounted. We introduce a focal strategy profile for these games, called the regular strategy profile, in which each sender reports sincerely, and the receiver stops if the number of stop messages exceeds a threshold. We prove that the regular strategy profile is a Perfect Bayesian Equilibrium (PBE) if the players are sufficiently patient.With this PBE as a focal equilibrium, we study the externalities that an additional sender may impose on the existing senders as well as the receiver.Perhaps surprisingly, an additional sender can have positive externality on the existing senders, and can also have negative externality on the receiver.