Dye Hair Black
A: Certainly. It's a simple matter to go from a lighter shade of hair color to a darker one, and doing so is much less harsh to the hair than color processes that lighten the hair as well. You should have little problem finding a hair color that will take you to black.
As a personal rule, I generally discourage anyone from trying to alter their hair color more than 3-4 shades. In most cases, changing the color more than this brings the hair out of the lightness/darkness range supported by the individual's skin tone. When the hair is too dark or light for the skin tone, the individual can look washed out and pasty. This isn't always the case, and it is largely a matter of personal preference.
You must also take into consideration the base color of the hair and try to keep the new color within that "family" of colors. A person whose hair is naturally a cool tone will often look pasty with a warm hair color, while those who have naturally warm hair color and change it to a cool color will find that they often look splotchy.
If you want to go darker, I suggest trying a graduated approach. Pick a shade of color in the same family as your natural color, but is 3-4 shades darker and try it as an intermediate step. If you like the color and it seems to work okay with your skin tone, you can go for an even darker shade later.
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See also:
Hair coloring
The 10 hair color shades
Cool and warm hair colors
Hair color and your skin tone