Large-scale sensor networks are used in modern applications to perform statistical inference. In particular, multiple change-point detection using a sensor network is of interest in applications, such as Internet of Things and environmental monitoring. In this paper, we consider deterministic multiple change-point detection using a sensor network, in which each sensor observes a different data stream and communicates with a fusion center (FC). Due to communication limitations, the fusion center monitors only a subset of the sensors at each time slot. We propose a detection procedure that takes into account these limitations. In this procedure, the FC monitors the sensors with the highest cumulative sum values under the communication limitations. It is shown that the proposed procedure is scalable in the sense that it attains an average detection delay (ADD) that does not increase with the number of sensors, while controlling the false discovery rate. Using the proposed procedure, we identify and analyze the tradeoff between reducing the ADD and reducing the average number of observations drawn until the change-points are declared.