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For a modern scientific look at color perceptions see Bimler's Psychological Color Space and Color Terms. Yes, you can imagine new "colors", and there are physically meaningful complex colors that humans don't really see.
Just so, can you imagine a color that doesn't exist?
Yes, an endless number of new (but currently non-existent) colors can be imagined. As many answers note, all colors only exist in the brain, and some colors we perceive are NOT directly related to a specific range of light waves.
Keeping this in view, how do we see new colors?
Impossible colors like reddish green or yellowish blue are trickier to see. To try to see these colors, put a yellow object and blue object right next to each other and cross your eyes so that the two objects overlap.
Red-green and yellow-blue are the so-called "forbidden colors." Composed of pairs of hues whose light frequencies automatically cancel each other out in the human eye, they're supposed to be impossible to see simultaneously. The limitation results from the way we perceive color in the first place.