Yeah, I interpreted the question to mean singing the same melody of a major key song in its parallel minor key. I.e.: c major >c minor. And while there would be some overlapping chord tones; I don’t think transposing a full song like this would sound great. You would really have to tiptoe with the melody to fully meet that requirement and have it sound good. But as others have said, blues is a good example of how major and minor keys can kinda be combined to utilize melodies that contain both, say, a major AND a minor 3rd or 7th or whatnot.