Not sure if this is
exactly what you were looking for, but I feel like my
Fandomstuck RP really captures that feeling of playing sort-of-canon characters without the restrictions that canon characters normally bring. (In fact, weren't you almost a member of Fandomstuck at one point? Your name seems familiar...)
Anywho! For anyone else reading, Fandomstuck's characters are all based off of entire fandoms as opposed to specific canon characters. Or, well, that's how it's usually introduced, but, to be honest, we usually don't place that much emphasis on how actual
fans behave
(mostly because that has the potential to become really mean-spirited...), and instead it becomes more about capturing the spirit of the series as a whole. So, the fandom characters are usually based pretty heavily off of the main character of their respective series (if not several characters), but, there's a lot more room for interpretation, because it's not supposed to be an exact replica of the canon version -- just something in the same general spirit of the canon. For example, one of the fandoms I play in the RP is Doctor Who -- who is not specifically based off of any particular incarnation of the canon Doctor, but rather, his personality is based more off of an amalgamation of basically all the incarnations. Moreover, there's the fact that these fandom characters don't share the same histories as their canon counterparts -- instead, they represent the history of the series as a whole. They exist for as long as it has existed. They're also self-aware -- not only aware that they're all based off of TV shows/video games/etc, but also being fans of those things, themselves. For example, Doctor Who is not thousands of years old -- rather, he's been around for about 50-odd years, following the show for all of that time through all its ups, downs, and hiatuses, and there's a lot of fun that can be had with how that sort of background combines with the canon you're working with. Going back to Doctor Who -- he's still pretty old by fandom standards, so he's still similar to the canon Doctor in that he's a lonely old man who's outlived so many of his old friends. There's also Steven Universe, who's very cheerful, optimistic, and innocent -- not just because canon Steven is this way, but also because the show itself is still so young and popular and hasn't suffered any major fall yet. And, hell, we even have Sonic the Hedgehog -- who, on the surface, has a personality that's basically identical to that of the canon Sonic, but he actually struggles with some pretty deep-seeded self-worth issues and feelings of inferiority from spending his whole life in Mario's shadow, all of which he constantly tries to bury and cover up with Sonic's over-the-top cool dude persona. XD There's just so much fun that can be had with it, and there's always so much more freedom than you have just playing a canon character alone.
BUT, that's a really specific example. As for more mundane stuff...
AU's. This is a pretty nice technique to utilize because, similarly to what happens in Fandomstuck, the characters' backstories change as a result of changing the world that they live in. So, again, you don't have as much of a strict canon to follow. Obviously characters that originally existed in a fantasy setting will behave rather differently in a realistic-fiction, modern-day high school AU -- but it's still possible to capture the personalities of those characters and therefore still feel like you're playing those canon characters. But, they're slightly different versions of them, which gives you a bit more room to play around in.
And lastly there's just... character development. A character can change as a result of what they go through
in the RP. So even if, upon starting an RP, you somehow manage to nail down a perfect replica of that character -- that perfect replica can change and therefore become a very different character than they started as just as a result of what they go through in the RP. Whether it's intentional or not, this is what I see happening to a lot of long-lived fandom RP's, as characters who were originally meant to be only canon characters sort of develop into more of their own thing over time.
