FWIW from the few studies about human tetrachromacy that I've heard of it seems that the women do in fact just see some similar-looking colors as more obviously distinct.

AIUI In order to see any "new" colors (i.e. outside the "visible" spectrum) they'd need to be more sensitive to UV or IR light (which in addition to being able to perceive those in isolation would presumably also mean being able to perceive those in combination, which indeed would drastically extend the numbers of colors).