In disaster operations management, the prepositioning of relief supplies might improve the efficiency of the corresponding operations significantly. Developing new strategies based on this idea for relief-supplies distribution operations might also provide great benefits because it allows the utilization of local resources in the critical time period after the occurrence of a disaster. Such local resources can be utilized to serve disaster victims until the arrivals of their central counterparts, usually organized by a governmental humanitarian organization. It is noted that two-stage stochastic programs provide a nice modeling framework for allocating disaster-response facilities for relief-supplies distribution in which facility allocation and service decisions are performed in the first and second stages, respectively. Although such a modeling framework is employed in a recent study for allocating temporary disaster-response facilities, it has some limitations in terms of representing the stochastic nature of the problem. In this paper, to point out these limitations, we extend the approach presented in the corresponding study by increasing the number of scenarios in the stochastic program via a more comprehensive scenario construction approach that considers the destructive effects of a disaster. In particular, we compute arrival time probabilities conditioned on disaster levels by modifying the mode parameter of a discrete-triangular mass function accordingly to represent different afterdisaster situations in the proposed scenario construction approach. A detailed case study to illustrate the extended approach is presented. It is noted from the results that considering the destructive effects of a disaster allows us to make new observations about the problem.