We present a three-stage method using mathematical-programming techniques for finding high-quality solutions to the multi-floor facility layout problem. The first stage is a linear mixed-integer program that assigns departments to floors such that the total of the vertical interaction costs between departments on different floors is globally minimized. Subsequent stages find a locally optimal layout for each floor. Two versions of the proposed approach are considered. The first solves the layout of each floor independently of the other floors, allowing up to one elevator location. The second solves the layout of all floors simultaneously and can handle multiple elevator locations. Preliminary computational results show that both versions of the proposed method can efficiently provide a good variety of high-quality solutions in a short amount of time for medium and large-scale problem instances.