Songs with same names won't add to "My Music"
Problem: You're on iOS and add to My Music a studio album from "Band X", with 10 different song titles. Then, if you try to add to My Music a live album or greatest hits type album from the same band, the new album will add fine to iOS, but when viewed in iTunes, any songs with the same name that are on the original album won't show in iTunes. It will only show the songs that don't exist on the original album. If you download the live album in iTunes instead of iOS, only songs with different names will download, and they won't appear in iOS.
Now here's where it's gets really interesting. If you remove one of the albums from My Music, such as the live album, iOS & iTunes will delete the album, plus, it'll delete any songs on any other album with the same name.
A good example to try is the band "Survivor" and the albums "Ultimate Survivor" 2004, 18 songs and Greatest Hits" 1993, 12 songs.