In order to unlock more songs for a particular playlist, you have to upgrade it! You can view the level progress for each playlist by visiting the music tab, denoted by the music note icon at the bottom left of your screen.

While on the music tab, you can view your playlist level & progress, indicated by the white bar & Level associated with the playlist. 

When you navigate to the individual playlist, you can view the progress & amount of available songs.

   

After reaching the next level for a playlist, you will see an indicator on the post-game recap screen.

In order to level the playlist to the next level, you must pay coins. Doing so will unlock some rewards as well as more songs for that playlist!