A stiffenable balloon catheter assembly capable of being converted from an “over-the-wire” mode with respect to a guidewire extending therethrough to a “rapid-exchange” mode with respect to a guidewire extending therethrough, and vice versa. The catheter has a plurality of lumens, one lumen however, having a side opening with an obstructable galp, the orientation of which, determines the utilization “mode” of the catheter assembly. Stiffening stylets may be adjustably locked into the lumens, depending upon the “mode”, to control the stiffness of the catheter assembly during its utilization within a patient.