Is it possible to add music to your Music Library on the iPhone? Possible use cases. Someone emails you a music demo. You find a song you want to download online. You want to download an MP3 from Soundcloud. 

It is easy to add songs to iTunes and sync it over with a computer, but is it possible to add songs to your Music Library on your actual phone? i
This is currently impossible. You can share downloaded audio with many apps - Dropbox, Google Drive, or the one I use most often for learning music and the like, forScore. But you can't share it with iTunes. Although, songs purchased on your phone can easily (or automatically) added to the libraries of your other Apple devices via Settings - iTunes &amp; App Store and selecting Music under Automatic Downloads.