Many years ago, just before Cats and I were married, we attended a bluegrass festival and one of the bands played a Beatles song bluegrass style. It worked really well, a lot better than I imagined. Here a couple of genre switching videos to get you thinking.
The most successful group you’ve never hear of doing genre switching IMHO is Postmodern Jukebox. They’ll take a Miley Cyrus song and turn it in to a jazz , a hip hop number into klezmer, etc… Really talented. Give this a try and you tube them for other creations later.