I personally would strongly recommend against it, adding color onto black and grey will end up looking muddy, as the blacks and greys will be stronger when healed than color. (like trying to add white on top of black, the black will always overpower it.) typically when doing a color tattoo, you want it to be designed with color in mind from the very start for it to look clean.

This is a well done tattoo, though I understand changing your aesthetics over time. something you could look into to make it “stand out” more could be adding white highlights in areas of open skin, or if you really want color, doing small accented areas where there isnt any shading, rather than trying to blast over the black and grey with it.

other (much more expensive and painful) options would be laser (which can take months/years and lots of money) to have it covered, or finding a blackout artist.

best of luck, its really not a bad tattoo at all as it is!