Can you apply semi permanent hair color on top of permanent hair color?

no your hair would not be able to handle it. semi - dyes stil dye and wen they wear off they stil leave a stain of the colour

Yes you can: always be sure to color after you perm, never perm a color. If it's a protein color you can have your stylist color your hair while it's being permed and the color will last significantly longer. Otherwise allow the perm to set before you have it colored.