The field of origami engineering has explored many multistable structures. One such structure is the Kresling origami, which is a pleated cylinder that can have stable deployed and compressed states. Much research has been done to understand the kinematics and mechanics of the Kresling unit cell. In comparison, the mechanics of towers consisting of stacked Kresling cells has been studied less. Here, we present a simple model which can accurately predict the load-displacement behavior of Kresling towers consisting of multiple, potentially distinct Kresling unit cells. In addition, the model reveals the presence of multiple stable states for certain tower heights. We then apply this theoretical understanding of Kresling towers to design a magnetically-reconfigurable metamaterial which exhibits tunable stiffness while maintaining a constant form factor.