No, Neopets cannot wear multiple NC Style items at the same time. If your pet is currently wearing an NC Style item, it will be replaced by the NC Prismatic Style item. For example, if you have a Nostalgic Baby Kougra, and apply a Prismatic Pink: Faerie Kougra item to it, the Nostalgic Baby Kougra style item will automatically be returned to your Styling Chamber, where you can apply it to another pet or place it in your inventory.