Transparency on overlapping 2D objects

I've got a 2D game with a character with overlapping 2D sprites (i.e. head, chest, legs, etc) so that you can switch out different looks.

I'm looking to create a portion of my game where you see a "ghost" version of the character. The problem is if I simply use the Alpha setting on the sprites to create semi-transparency, you can now see that the parts are in fact overlapping and it looks terrible. Is there a way to apply a form of transparency to a parent object which makes the entire character as displayed become semi transparent rather than the individual pieces?