FIX-UP.  Yes!  We frequently touch up, repair and rework old, faded or poorly done tattoos.
COVER-UP.  Yes!  We cover up old, unwanted tattoos all the time.  With a personal consultation, your artist will evaluate your project and direct you towards a tattoo you will be happy to look at forever!
COVER-UP FACTORS TO CONSIDER:  1) Nothing covers dark ink better than dark ink.  2) It is very difficult to "lighten up" dark tattooed areas.  Often when a light color is tattooed over a darker color, the dark color will show through after healing.  If the goal is to "lighten" and area, it may take more that one application of the lighter color.  3) Tattoo ink does not work like paint where one layer completely covers another layer.  4) In some difficult cases, using a laser to remove or lighten all or parts of the offending old tattoo may be suggested as the best option.  5) Often the new tattoo will be larger than the original to allow for the cover up.  6) You will never cover a tribal with a Christ Head!  You just can't.
As always your project is best discussed with your artist.