That image looks squished. Reverse Google Image search turned up
this other version, which is wider and more in line with other faces from the show.
Desaturating the jacket would help, but it would probably teach you less about colour harmony than trying to get the blue to work would. Hue-shifting isn't merely a stylistic thing, it's a matter of light in the scene too. Shadows shift towards the ambient light in the scene, highlights shift towards the key light.
Here's an edit reducing the banding:
Try putting it as a layer over your version and toggling between the two to help you spot the differences. The key thing is just avoiding areas where pixels line up, such as by shifting some things over, using larger or smaller AA, or simply not AAing when it isn't necessary.
In addition to reducing the banding, I made some other changes:
- Reduced the brightness of the 2nd lightest skin tone (reused a colour from his eyes), which makes it more suitable as AA on the face and makes it stand out a bit less in the rim light on the dark side of the neck.
- Made the rim lights on the neck and shoulders fade off a bit so they're less prominent. This helps keep the focus on the face, and makes the jacket look like it's actually on his body rather than pasted above it, because it now casts a shadow on him.
- Darkened the bright ear a little. It was distractingly bright before, I think this change is better for the overall composition. I did the same with the small highlight on his cheek, it looked like it was sticking out too much.
- Smoothed some curves on the hair. There's more work you could do with that, hopefully my edits give you some ideas.