Yes, artists can mint as many NFTs as they please for the same artwork. Of course, most usually don’t do that to keep the digital art piece scarce and rare, ensuring competition for ownership. 

However, artists sometimes release limited editions, such as 10 NFTs of the same artwork or what is known as open editions. With open editions, there will be a time frame, for example, five minutes, during which anyone can purchase the artwork on sale, and there will be as many pieces minted as were bought in that time frame.

Open editions are generally considered to be less prestigious as there are a lot of people who will own the same NFT artwork, making it less valuable. So while you can launch multiple NFTs for the same digital artwork, there are pros and cons.