Is there cosmetic surgery for people with Down syndrome to hide their down appearance?

Described procedures. Numerous procedures have been described for advanced forms which focus on either the eye appearance or the tongue protrusion.
Yes, but is not done. Since there are many thousands of people with down syndrome, and they all have down syndrome physical features, their appearance is pretty well accepted in our society. Cosmetic surgery, therefore, is generally not used to alter their features. Also, it would be hard to communicate with a down syndrome person (due to limited intelligence) about why any cosmetic procedure would be helpful.