Permanent & Semi-Permanent Hair Color
A: Permanent color can always be applied over semi-permanent color, and the time needed to be taken between color applications depends on the condition of the hair in question. Barring any signs of damage to the hair, you could conceivable be safe in applying a permanent color immediately following the application of a semi-permanent one.
The reverse, however, is not universally true. You can only apply a semi-permanent color over a permanent color if the semi-permanent color is darker than the permanent color. Permanent color formulas may contain hydrogen peroxide developer of a strength sufficient to actually lift the color of the hair to which it is being applied before the color is actually deposited.
Semi-permanent color never provides any lifting action to the hair and therefore cannot be used to lighten the hair whether the hair has been colored with permanent color or not.
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See also:
The base color of your hair
The different types of hair coloring
How to color hair
Hair color levels and peroxide developer