How many songs can I have in my Apple Music Library?

Anyone know why there are certain songs that you can only stream and not add to your library? I have my account set up to automatically download the song after I click Add to Library so they are always there and I can play them when I'm offline. So I click the three dots next to song, click Add to Library and nothing happens. It is the same thing through the iPad or on iTunes. I've read that if you reach a certain number (usually in the hundreds of thousands) in your library it won't let you add anymore. I currently only have about 3,000 songs in my library

[Re-Titled by Moderator]