Step 6: Extending it
With the analog inputs having a 10 bit resolution, that gives us 1023 values between 0V and the reference voltage. If you divide that by 12 buttons, you can see that each button would have to be within a unique range of 85 points. I would call it no more than 40 - 50 to be safe.
If you do this, you would have to use fairly accurate resistors (Or measure them and use the ones that are close to the E12 vaues) and you would quite possibly need a better way to debounce the buttons.
From the fact that all my values are within a maximum range of 11 points, this seems completely doable.