You need a magisterially-oversized outer layer.

I would probably start with a secondhand oversized, double-breasted wool greatcoat from Stella McCartney or Isabel Marant, in an old-man windowpane or houndstooth if available; you want something with a big-ass collar you can turn up when you're solving mysteries, and sleeves so generous they crumple when you have your hands in your pockets. Then add a few lapel pins, band buttons if you're feeling bratty or something vintage and heavy or just plain old weird if you want to send diplomatic messages like Madeleine Albright. A beautifully-made coat with a strong silhouette scaled up to a seriously-irresponsible fit elevates anything under it, even if you're starkers.