Three key pieces:
-Microsoft IntelliMouse (or any variation thereof)
-Wlonk chordkey system
-Bare-bones driver
The first two are around already.
A driver would need to be developed. Such a driver would not be difficult. We're not talking about dual cursors or anything. That comes
later, when the idea gains popularity sufficient to pressure tech companies into spending more bucks to develop a really fancy driver.
Ten total buttons (one per finger) allows extensive customization, and would allow a ten-button chordkey typing system to work easily. The Wlonk system would be used simply because of its jaw-dropping learning curve. A stenography system (coupling shorthand with chordkeying) would be easily programmed as an option for those who cared to learn it.
IntelliMice can already send simultaneous clicks, but I don't know if they can do so for any combination of buttons. E.g. in Minesweeper a left/right click on a number will clear all unmarked adjacent squares if the number of adjacent mines marked is the same as the number clicked. I don't know if the current hardware supports thumb/scrollwheel clicks, or thumb/left/right/pinky clicks. If not, it would be trivial.
Possible Hardware Extensions:
-Cordless/Bluetooth
-Optical/gyroscopic
-Self-powered (numerous ways suggested)
-Better-feeling buttons/keys (thumb/pinky/scrollwheel especially)
-Quieter buttons/keys
-USB/PS2 splitter (two mice in one port)
-Eliminate scrollwheel in favor of button (a click with this (or another) button could have the same dot-on-screen-scrolling-effect as a click with the scrollwheel currently does)
Possible Software Extensions:
-Open-source drivers
-Two cursors
-Integration with operating systems
-Integration with gaming
-Integration with drawing, painting, CAD