Why do you want to buy a screen protector for the screen protector?
Why do I wear two pair of nitrile gloves in the lab?
Do the manufacturers explicitly support this?
Sometimes, wearing two layers of such things (such as condoms) increases the risk of failure because the material is not made to be used next to another layer of itself in that fashion.
So if you are doing so without explicit support from the manufacturer then you could quite easily be increasing your risk through foolishness.
And the reference here to condoms is quite deliberate as there is an urban myth in some parts that wearing two increases your protection because if one fails then the other is still in tact. The problem here is that condoms are designed and manufactured with the expectation that both sides of a condom will come into contact with skin when friction is being applied. When one side comes into contact with other condom material, the chance of failure goes up.http://www.health.arizona.edu/health_topics/sexual_health/usingtwocondoms.htm
seems to suggest that wearing thicker gloves offer the same level of protection that wearing double gloves gives.
Now all of that has nothing to do with using a protector for the protector.
The common misbelief is that the surface on the back of Canon cameras is an LCD surface as it is with Nikon cameras. That is incorrect. Canon build into the camera an LCD screen protector that is easily and cheaply replaced.