Everything in a mouse is done inside the chip. If the chip is designed for use in other models of mice that have more buttons, it may have pins that you can connect to extra buttons. But if it doesn't, you don't have any options.
As Kris has mentioned, the chip inside the Mouse will determine what you can or can't
easily accomplish. Worst case, if you can't tie additional buttons into the mouse, you can stuff extra hardware in the mouse.
There are example projects online that show you how to program a PIC, AVR, Arduino, etc. to act as a HID. (Human Interface Device) If your willing to do this you can add as many buttons as you can physically fit. To avoid having to mess with the optical tracking... just cram the internals from a small usb hub inside the mouse as well. Mouse and your Microcontroller get wired to the hub, and the hub gets wired to the mouse's original wire to the computer.
This trick has been used to hide mass storage devices in mice, it can easily be adapted to add an additional HID device.