Minor changes are usually possible without incident. However, reducing thickness MAY leave the restoration too thin and prone to break. It also may result in a loss of "gloss" or "sheen", and polishing may not get back to what it was. In that case, remaking is best. I would START with adjusting it, but know that remake may be needed.

Hi:Most of the time it is possible to do minor adjustment on the crown and veneer surface. It’s best to go back to your dentist and voice your concern.Best,Dr. Maddahi

If the crown is made of porcelain with a metal substructure, the porcelain needs to be a certain thickness for strength and to cover the metal alloy underneath. If shaved too much, the metal may begin to show through and/or the porcelain will fracture. If the crown is made of only porcelain or Zirconia, then it may be possible to smooth down to where you like it. That being said, I agree with Dr. Timmerman that be prepared the tooth may need a new crown.