I have a country bounded on three sides by fold mountains. Due to a magical plot device, the force acting to drive the upward motion of the mountains persists indefinitely, acting on the plates outside of the one my country sits on. The same magic prevents any damage (weathering, melting, etc) to the central plate. I believe that as the mountains increase in height they will weigh more and therefore sink deeper into the mantle where the base would melt. This should lead to a balance eventually being reached dependent on the type of rock, the rate of mountain top weathering, the speed at which the tectonic plates are forced up, the temperature of the mantle etc.
Playing through the various factors leads me to believe at doubling the speed would not double the height attained and there would be an absolute limit that could be attained.
Am I right in coming to that conclusion that the growth rate influences the maximum height of a mountain and if so are you able to suggest what height that would be? (limitations: Assume this takes place on earth with the same crust composition and gravity)