@Michael Le, I had a thought about a way you might be able to do this on the keyboard rather than in a DAW, but I've no way to try it myself since I don't have a DGX-660. It would still require using an additional device such as a computer or phone, but if you'd rather not get too involved with DAWs then this should be simpler (if it works):
1) Record a User Song-- which I think you've already done?
2) Convert the User Song to an audio file on an attached USB flash drive.
3) Plug the USB flash drive into your computer or other device; if you're lucky, you might even be able to connect the USB flash drive to your smartphone if you've got a suitable adapter.
4) Connect the computer or other device to the keyboard by plugging one end of an auxiliary audio cable into the headphones jack of the computer/device and plugging the other end into the AUX IN jack of the keybiard.
5) Connect a microphone as well.
6) Use the procedure for recording directly to an audio file while playing back the existing audio file and singing along with it. I'm not certain that the keyboard will let you mix the audio from the AUX IN connection with the audio from the microphone, but I don't see why it shouldn't. I'm also not certain whether you need to be playing something on the keyboard while doing this, but I don't see why it should.