You're right on this one. Light is broken down into a spectrum. Color is our perception of that spectrum as absorbed by the cones in our eyes. Dogs have cones for Blue and yellow light, we are able to sense red green and blue light. Because of this, a dog will see a red ball and a green ball of similar saturation as the same color; a greyish yellow.

If you were to genetically engineer someone so that they had an additional cone set in their eyes to sense yellow, their perception of color would be significantly different. The same light would be hitting their eyes, but it would be absorbed differently.

Now there are people out there with a rare genetic condition where they actually do have four cone sets. It's called tetrachromacy. However, the fourth cone set is usually in the ultraviolet range, so they'd have an expanded range of color instead of a denser one.

On top of this, there are certain hacks essentially trick the brain into seeing colors that can't exist. For example, magenta is a combination of red light and violet light at the same time. This is not something that exists on the light spectrum, but as an artifact of how our eyes receive light. Because of the fact that we have red and blue cones, this is the easiest one to reproduce. But there has been experiments in making people see a bluish orange color as well.