In one aspect, the present disclosure concerns a percutaneously delivered adapter stent that is deployed within a previously implanted prosthetic valve and serves as an anchor or platform for implanting a percutaneously delivered replacement valve within the previously implanted valve. The adapter stent can be delivered to the implantation site via the patient's vasculature and positioned within the previously implanted valve. The stent can then be deployed to cause the stent to expand and become anchored to the inner surface of the previously implanted valve. Subsequently, the replacement valve can be positioned within the adapter stent and deployed to cause the replacement valve to expand and become anchored to the adapter stent. The adapter stent and the replacement valve can be mounted on the same catheter for delivery to the implantation site.