VGA Split

I was wondering if it is even possible to split VGA signals. Now, this may seem weird, I want 2 inputs to 1 output. Is this possible. The idea is I have an external monitor for my iMac. I have it connected via miniDisplay Port -> VGA. I also have a video processor (thing) - (it is able to have an Audio/Video input, antenna input, etc). I want to be able to use the single VGA monitor and switch between the two inputs when I want to use it as an extended monitor, or to play videogames/TV/etc on.

If this is possible, I would like to know, and if so, where/what do I need to make it happen.

Input----____
aaaaaaa ____------Output
Input----

Thanks!