How to Add All Songs of Apple Music Playlist to My Music at Once?

2021, iTunes got replaced by Music.

1. Add playlist any way you do it (I migrated from another streaming platform)
2. Open Music and go to this playlist. Make sure it's open in Music - songs get 100% of playlist window
3. Command + A -> Add to Library

The + sign is no longer in apple music on playlists I have created. I found a different solution on my own by opening Apple Music on my laptop, clicking file in the top left corner, clicking Add to library, then selecting my Music Folder on the side bar, then clicking the desired playlist, and finally, selecting all the songs in the playlist and clicking Open. To get the same thing to happen on your phone, follow these steps while your phone is connected to your computer through USB. Then (on your computer), go to recently added on your apple music library sidebar, and highlight every album. Right click one of the albums and click "add to my music". Your playlist should be successfully imported into your library!

I finally found the solution.

Here are the steps to force iTunes to add all songs of an Apple Music Playlist to your local iTunes “My Music” library:

1. Add the Apple Music Playlist to your library by clicking on the + icon on the upper right.
2. Go to the Playlists tab and select the recently added Apple Music Playlist. Now select all tracks and right click on any of them to select “New Playlist from Selection”.
3. After iTunes has created a new playlist, go back to the original one to select all tracks again and drag them over to your new playlists. Skip adding duplicates.
4. You’re done - now all these tracks should be added to your local iTunes “My Music” libray and you can safely delete both playlists!

Easier option (from iMac):

1. Add the Apple Music Playlist to your library by clicking on the + icon on the upper right.
2. Now that this new playlist appears in your left tab with all your playlists, drag it to your other playlist

Yes you can, on both iTunes and your Apple device. You didn't mention which device specifically, but on iTunes, look for the + icon or the ..., which you can click and Add to My Music as well.

Check out these screenshots below on iTunes. I boxed the + icon on both pictures because that is the simpler approach, but you can also click the ...: