Actually, you can do this on Genos but *only* if you are recording Audio, not recording MIDI.
Open the Song Player, set song A to Audio and load up the audio file. Then press Recording, and select Audio Quick Recording.
Touch the buttons on the screen to start recording, press 'play' on the panel for Song A, and then play your part along with it. Both the audio and your playing will end up in the new recorded file.