Surely parody songs are plagiarism in essence anyway, and usually fraught with copyright issues? Nevertheless, it’s very easy with a true parody - playing around with the original lyrics - to find that someone has already done similar, but then you’re not being original anyway if you are basing your song on a previous one. Don’t get me wrong here, I love parodies and have produced dozens myself, without intending to denigrate the original - like with comedy impersonators, we are only rude the ones we love.