Thanks for reaching out about this and welcome to the Community.
Could you let us know what exactly happens when you try adding new songs to your playlists? Also, having large playlists might interfere with the app's performance on your device. We usually recommend to split the songs out in smaller playlists, this would make it easier.
On another note, keep in mind that the download limit is 10,000 songs per device on up to 5 devices. It looks like other users would like to change that and posted this idea requesting it. You can add your support there by up-voting the idea. We'll inform on any developments there, as soon as there are any. So make sure to subscribe, if you haven't already.
We'll be on the lookout 🙂
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“Music acts like a magic key, to which the most tightly closed heart opens.”– Maria von Trapp