Take a look at this topic that I posted:
Even though that topic may not be what you’re interested in, you may be interested in the “minkey.blend” file that you can download there.
If you open “minkey.blend” you’ll see that I have created keys for the upper and lower eyelids. However because keys move in a linear fashion I used two keys for the upper eyelid to prevent exactly what you are saying (eyelid cutting through the white). I have then linked all the keys to the slider (bottom right of the screen) and it doesn’t cut through the white.
It is necessary to ramp the first “halfway” key from 0 to 1 and then back to 0 again as the second key takes over. Take a look at the ipos in the window on the right in “minkey.blend” and you’ll see what I mean.
I think this is exactly the method Sketchy mentioned above.
Hope this helps,
PS. Once you’re happy with your eyes, you may then be interested in looking at the above topic (https://blenderartists.org/forum/viewtopic.php?t=59721) when you try to fathom out how to make mods in your base shape and get them to appear in the edit meshes for each of the keys.