Sender-based message logging (SBML) is one of the most lightweight fault-tolerance techniques to considerably lower high failure-free overhead of receiver-based message logging by using volatile memory of its sender as storage for logging. However, all of the existing SBML protocols have the limitation that they can tolerate only a single failure at one time, called sequential failures. So, if more than one process crashes concurrently, they may not make the entire system consistent. Assuming reliable FIFO point-to-point communication links, all the existing SBML protocols may not effectively employ log information of the same message to a group its members received on being applied into group communication link-based distributed system platforms. This paper presents a new SBML protocol to tolerate concurrent failures by using the inherently beneficial features of FIFO broadcast links effectively. The protocol can lift the inherent drawback of the original SBML by replicating the log information of each message sent to a group into the volatile storages of its members. Therefore, even if only one process in a group survives at a time, our protocol can progress the execution of the entire system without stopping and restarting it.