Q:

How to set only black to overprint on embedded image on Adobe Illustrator

I have an embedded image on an AI file.  The image was originally a Photoshop file.  I linked it, embedded it, turned it into grey-scale, I set its colour to 100% K (black). 

The black and white character is the embedded image.  The background is a flat PMS ink.  
The character should be printed using only black (K), not using white ink as well.  The white area should be knocked out from the blue.  
If the black ink is not overprinted on the blue, its fur will look weird.  It is too thin to be knocked out from the blue. 
I cannot set the whole image to overprint (or multiply), because then the white area would disappear. 

I also Edit->Edit Colours->Overprint Black but I get the message "None of the selected objects are painted the specified percentage of black"
Is there a way to indicate that ONLY the black of the embedded image should overprint?  

A:

Raster images are treated as a whole.  You can't specify plate interaction within raster images. 
If it were me, I'd use the black from Photoshop and set it to overprint, then draw a white shape in Illustrator behinds the raster and group the two.