Eleven and a half year old spoiler: The character Thomas Anderson / "Neo" is apparently dead at the end of The Matrix trilogy, with the vague hope that he -- like any other messiah-type figure -- isn't really dead. So my headcanon goes, the machines have resurrected and modified several copies of Neo and placed them in varying parts of the super-city of the Matrix. For example:
Constantine (2005): This Neo exorcises demon programs and interacts with the angels from a previous version of the Matrix, similar to Seraph (Collin Chou) in the canonical films. The original Neo's mastery over the Matrix gives this version the power to use magic and magical items.
Man of Tai Chi (2013): This Neo lived long enough to become a villain. It's up to the next would-be One (Tiger Hu Chen) to stop him.
47 Ronin (2013): This Neo ended up as a foundling in the feudal Japan part of the Matrix's super-city. Since Neo is a special Matrix character, he is able to interact with forest demons, remnants from a past version of the Matrix. Like almost all other Neos, this one can do some magical stuff.
John Wick (2014): This version of Neo is sad. He lost his wife. He also lost his puppy and his car because Theon Greyjoy (Alfie Allen) makes poor decisions. Damnit, Reek! It's okay, though; this Neo thrives on getting his revenge.
It seems every action movie starring Keanu Reeves gives his character god-like martial arts moves, just like Neo in the actual Matrix films. Identifying these various characters as Neo himself makes it easy to explain why this Keanu character or that Keanu character can kick ass so efficiently. He's not a trained hitman; he's Neo. He's not a morally corrupt, rich martial arts enthusiast; he's Neo. He's not a village outcast who picked up some samurai training along the way; he's Neo. He doesn't dabble in the occult; he's Neo.
In conclusion, as long as Keanu Reeves stars in action movies featuring innovative, albeit impossible, versions of martial arts, then who needs another official Matrix movie?
They're all Matrix movies, and they're all fun to watch.