That's true Napster did get shut down but correct me if i'm wrong but there should be more things that people can share other than copyrighted material. Still it's just a very rough idea at this point in time so comments are still welcome. Thanks.
Yes, there can be but you know, people love sharing copyrighted materials like games, movies and etc. Despite the fact that Napster had issues, you can adapt something like Youtube has for protecting copyrights (idk how is that possible or even whether that's possible but just saying if it's). Or also maybe including button of copyright abuse can help a little.
Otherwise only deal in this situation to my mind is to operate that business in DMCA ignored places like Russia for example but in this case you have to get rid of their copyrighted materials I guess.