Color does not lift (lighten) a previously applied color. It's a simple rule that all stylists have had drilled into them. You can deposit color onto hair and add different tones all you like, but you cannot lift the hair a single shade if it has been dyed previously.
It is very simple to color over hair that has been previously colored—if you are going darker. All you have to do is apply the color, process it and enjoy the results.
It is also possible to tweak the color just a bit. If you desire a redder tone, for instance, you can add red tones to the color provided that the color is not too overpowering to allow the red tones to shine through.
You cannot lift hair color with hair color. You must pre-lighten, or bleach out, the existing color before you can apply more color.
It is always advisable to perform a strand test on hair that has been previously dyed to see if it is feasible to dye it again. To perform a strand test, cut out a small strand of hair and apply the desired color to the hair. Process the hair, and check the results.
In some cases, color-treated hair is not strong enough to withstand another color application. You must always make sure that another color application will not damage hair beyond repair before applying more color.