Reading the Best Bond story on the mainpage reminded me that in 1983, there was not one 007 movie, but two: Octopussy, starring Roger Moore as Bond from the Broccoli family's EON Productions, released by MGM/UA in June, and the independently-produced Never Say Never Again, with Sean Connery reprising the role for the first time since 1971's Diamonds Are Forever, distributed by Warner Bros. in October.
As a kid, I was never a huge fan of the character, but it was really exciting to have two Bond movies in the same year, even if, technically, they weren't part of the same series. Never Say Never Again was a loose remake of 1964's Thunderball; through a legal loophole, producer and cowriter Kevin McClory was able to produce his own iterations of the story without impinging on the Broccolis' screen rights to the Fleming novels. Even though it starred the iconic Connery as Bond, the movie couldn't feature any of the signature elements that defined the "official" series: No Monty Norman theme song, no "gun barrel" opening, and different actors in the roles of Q, M, and Moneypenny. It is, however, the only Bond movie from the '80s to feature Blofeld and SPECTRE, or at least be able to identify them by name (a Blofeld-like character puts in a brief appearance in the opening of For Your Eyes Only); McClory owned the rights to those characters, and only in the last few years have they returned to the "real" Bond stable.
Even so, Never Say Never Again felt like a Bond movie to me, and I enjoyed it a lot more than the convoluted, boring Octopussy. It was full of action, humor, beautiful women (including a young Kim Basinger), exotic scenery, and a lot of double entendres and one-liners. And it had that kick-ass World Domination video game. Connery looks visibly aged in some scenes, but he comes off as weathered and experienced where Moore just looked too old in his '80s movies. I remember being really excited about the idea of two separate Bond series, and hoped that Connery might continue to play the character, but alas, it was not to be.
Still, I have to wonder if there isn't some value in the idea of having multiple franchises about the same character at the same time, even if they directly conflict one another's vision of what the character is supposed to be. It happens in comics and video games all the time: Consider the "Ultimate" line of Marvel's heroes, or the various incarnations of Link from the Zelda games. Think also of the various animated incarnations of popular characters from other media, such as the different Batman cartoons. Or more recently, the live action DC shows, such as Arrow, The Flash, Gotham, and Constantine, all of which theoretically could fit into an MCU-style framework, but appear for the moment to exist independently of each others and the filmic DC universe. And on top of that, consider the various reboots, soft and otherwise, of long-running properties like Bond, Batman, and Star Trek (which at one point featured three very different, though loosely intertwined, movie and television series).
So why not have different movie series based on the same properties running concurrently? Batman is a great example. You could have a more comic book-y, "in-universe" Batman, a darker, more "realistic" Batman with no other superheroes, or even a silly, self-aware Batman reminiscent of the Adam West show and The Brave and the Bold. There's certainly a risk that audiences might get confused, but if the different versions were stylistically and tonally distinct enough it wouldn't be much of a problem. Most moviegoers aren't as hung up on continuity and other fan orthodoxies; they just want to have fun. It wouldn't be all that hard to distinguish a "serious" Batman from a silly Batman, any more than it was that hard to tell Sean Connery apart from Roger Moore.