I added on the owl's body mor thin glazes of gray, gray + ultramarine and gray + natural sienna, with different value depending on the spot. I worked especially around the facial mask which looked weird. I also added more layers to the background (gray, sienna, magenta) but it looked a bit dull and confusing, so I later decided to cover it completely with desaturated magenta, and also darken the areas of black + ultrmarine on the top and bottom right.
And this is the final version, after adding more glazing (especially sienna on the body and wings) and puttin gin more pure white for highlights and black/dark grey + ultramarine for deep shadows:
Color corrected to look more like the real one, although its look depends a lot on the lights of the room.
PS: just found a photo of the real thing...