I would look at it the other way around. There is an infinite spectrum of light that we see every day. The limiting factor is our brain interpreting and categorizing this spectrum. The only reason we see stripes on a rainbow, is because our brain can only come up with so many colors to fill in the infinite gradations between the wavelenghts of light.

I would say, its your brain that limits what colors you see, so it would be impossible to come up with a new one.

If you did happen to invent a new color in a dream, your brain would probably associate it to a certain wavelength of light in the real world, and you would start seeing it all the time.

What's interesting to me, as an artist, is that everyone sees color differently. Men are more responsive to cool colors (greens and blues) compared to women, who are more stimulated by warm (reds and pinks). This is not just a trained environmental bias. Men can see further into the ultraviolet end of the spectrum, and women can see the opposite- towards the infrared.

Imagine this- if my eyes are genetically more tuned to the long wavelength end of the spectrum, than the blue that I see, you would see as purple. The Green that I see, you would see as blue, and the red that I see, you would not even have a name for.