I think it might be kind of cool to follow a long term story, centered around James Gordon. He could solve crimes, which span several issues. The kind of crimes which might still involve murder, but it's a bit below Batman's "pay grade" as it were.
No Joker. No big name villains....most of the time. You might go several issues without Batman. But during certain story arcs, when things are at their bleakest, Gordon could call on Batman via the Bat signal.
And maybe they could run a paralell comic centered on Batman. And they would always be the same issue number. Batman #1 releases same day as Gordon #1.
That way, whatever interactions Batman and Gordon have, are exactly the same in both comics. Which is why their interactions would be brief. Reading Gordon, you'd see the events from his perspective, and reading Batman, you'd see the story through his perspective....and they wouldn't even be the same story.
Actually.....we could go bigger. Imagine if they had 10 different comics running at the same time. Where you have 10 different stories, all set in Gotham, but they are 10 different stories.
So you might be reading Catwoman, and Selina Kyle happens to see on the news that Batman arrested Harvey Dent. It's not part of her story, it's just one or two panels of something that happens to be on the news. Meanwhile, over on the Batman comic, its a whole story.
So the idea would be the city is alive. Yes, I started this post thinking about just dedicated to Gordon, but just fleshing the idea out as I type, and I made it more about the city, than any individual. His comic would be about him, but the series would be about Gotham. Events taking place in a city of interconnected characters, even when they aren't connected.
So you could know on April 5th, at 9pm, Batman is fighting the Joker, but Gordon is drinking in his office after having a mental breakdown over emotions regarding Barbra being newly wheelchair bound. Meanwhile in another comic, Nightwing is intensifying his training, and trying to cope with the difficulty of reinventing himself from Robin to Nightwing. Meanwhile Harvey Dent (not yet twoface) is preparing a speech to deliver in court.
All seperate comics. And if the stories intersect, so be it, but that's not the point.
Have they ever done anything like that?
Beat cop IIRC, it's been a minute.