I've been thinking about a dynamic keyboard where each key is a tiny oled screen that shows what character you're going to type in this particular mode. And then you're free to switch from regular to math to Greek to Chinese if you want, and the keyboard simply adjusts.
Such as Optimus Maximus, for example?
For example, on Windows I use Wincompose [1], that lets me type things like "⋄*g" for Greek gamma: 'γ', or "⋄ee" for 'ə', or even "⋄⋄plane" for a '' (and of course the list is customizable). The "⋄" symbol represents the Compose key, which I chose to map to the Caps Lock key on my keyboard.
[1] http://wincompose.info/
Edit: HN removed the airplane icon.