One director I thought of that doesn't necessarily have A thing but more like two extraordinarily different things, is David Gordon Green.  To wit:

George Washington
All the Real Girls
Snow Angels
Pineapple Express
Your Highness
The Sitter

...and oh by the way, he's the Executive Producer of Eastbound and Down.

And OMIGOD James Mangold directed Heavy?  Check it out if you've ever seen it.  It is a bizarre, sad, little film.

John Woo is another director who has a distinct style, or used to have. You can definitely see a common style between Hard Target, Face Off and Mission Impossible 2, though these are admittedly an over-emphasized version of the style in his early Hong Kong films (e.g. The Killer, Hard Boiled).

Teague is a Nerdfighter?

You know I always felt that the Coen Bros' thing was: We live in an absurd world. I mean just look at how they portray violence.

Vampire David Bowie? VAMPIRE DAVID BOWIE?

-regains composure-

I've been thinking if there's anything in the distinction between what makes someone a good director vs. a good filmmaker. A good director can make an excellent movie, but the result will never be better than the script. Whereas, a good filmmaker bends all of the disciplines that go into making a movie towards something, uh, want to say, "greater than the sum of its parts", but that would put this bullshit thought way over the edge. Oof, sorry to get so Bresson-y.

Tarantino wrote the screenplay for True Romance (good film btw, check it out Trey, especially if you like Walken, and Patricia Arquette, so hot)

I was saying Cronenberg the entire pod, and he stepped out of his "thing" with Straight Story.

Lynch! Yes