Really you are better off removing the old heatsink/fan unit and fitting a bigger/better one in its place.
Stacking heatsinks may give you a bit more heat dissipation from the chip, but the transfer from one heatsink to the other will not be efficient as the hedgehog/fin patterns give better surface area exposure to air, and is definitely not the best way of metal->metal heat transfer (which would be most efficient with flat surfaces).