Multicolor LED based on different input voltages
You could do that, but you wouldn't get to pick the colors or voltages.

For example, if you got an RGB LED (actually 3 LEDs in one package) and connected them all in parallel, the red one would be the first to illuminate at its rated forward voltage.  Second to illuminate would be the green, giving you a yellow or orange hue.  Finally, when you reached the forward voltage of the blue LED, you might see something approaching white.

Without additional circuitry, you don't have much control of the threshold voltages or colors other than part selection.