In humans, effectively no. Anyone claiming to be a "tetrachromat" is really trying to say they're half-colorblind, that they have some normal and some mutated green cones. If they do, the mutated green cones basically don't work.

Mantis shrimp have 12 different types of cone cells to our 3. Now, some people want to think that they either see a wider rainbow, or have significantly greater resolution or depth of color perception than we do. The former is kind of true, the latter very much isn't. Humans have VERY sophisticated brains, we use more brain matter than the mantis shrimp's entire mass to process vision. We do all kinds of Nvidia branded shit to turn the three color signals from our eyes into the full spectrum of colors we perceive. Meanwhile, the mantis shrimp sees in EGA. They see 12 colors...only, and at a much lower resolution than we do with their compound eyes.