OnSong provides a number of ways to build your sets.  If you're looking to review songs in one set and place them into another, the Organizer Menu can be a helpful tool.  Load the set where the song is placed and flip through the set using the Song Viewer. When you reach a song that you'd like to add to another set, tap on the "star" icon in the Menubar to open the Organizer Menu.  Tap on the Sets tab to view a list of Active and Archived sets.  This allows you to see the sets that song is in.  You can also tap on the set to add or remove the song.

You can also move songs between areas in the app using Drag and Drop on iOS 11 and higher.

Please note that if you have received a set from another user, the songs may be loaned.  If the song is loaned, it is not available in your library and will not be able to be added to other sets.  The person who shared the song with you will need to ensure they have the right to distribute that song to you and they can turn off loan shared songs.