Spin-offs are a long-standing tradition in television, but generally the new shows stick quite closely to the aesthetics of the old. The Flash is much lighter in tone than Arrow, but it's still fundamentally about a crime-fighter taking down a bad guy each week with the help of a group of friends/specialists. The various Star Trek shows were all cut from the same mold, Friends and Joey were both sitcoms, etc. Even Doctor Who, which spawned the family-friendly Sarah Jane Adventures and the more adult Torchwood, kept all three shows within the "alien/sci-fi adventures and mysteries" world.
But have there been any shows which spawned spin-offs, set in the same universe and featuring related characters, but with entirely different genres and structures? A police procedural with a spinoff sitcom about the cop's daughter, for example, or medical drama that spun-off into a sci-fi adventure?