From time to time (and increasingly often these days, it seems) I’ll be listening to a song and find that a completely different song is running through my head — and that, against all odds, it works — that, with a few adjustments to the tempo and the key, the two songs sound good sung simultaneously.
To see what I mean, try this. Play “Look Out (Here Comes Tomorrow)” by the Monkees,
and while it’s playing, try to sing “Country Roads” by John Denver.
You’ll have to sing it quite a bit faster than John Denver does, and it can be a challenge to keep to the tune and not be distracted by what the Monkees are singing, but after a few tries you should be able to get it. (You should be singing “Country roads / take me home / to the place / where I was born” in sync with “I see / all kinds of sorrow / wish I / only loved one.”) If I had any musical talent I’d record the combination myself, but I don’t, so you’ll just have to try it yourself.
Here’s another you can try: “Climbing the Walls” by They Might Be Giants
and “Moonshadow” by Cat Stevens.
I find that for both of these mixes, the two songs go together lyrically as well as melodically.