You could canonize the entire series as well with Bourne's hazy flash backs. The one downfall this series has is each film storyline is focused around a new memory that Bourne has. If you could link all those memories, feeding us pieces of each memory from the start of THE BOURNE IDENTITY, the films would fall together nicely. Toward the climax of each film, one memory would crystalize more and he has more information.
In addition, I'd like to see the end of THE BOURNE SUPREMACY end with Jason apologizing to Marie's brother. Seems like a much more fitting end. You can keep the apology to the Neskey girl, thats fine. Just replace the end conversation with Pam Landy with Marie's brother. There is a line in that conversation where Bourne says something about finding the person responsible, that was there from the start. That's a great cliffhangef for THE BOURNE ULTIMATUM.
Plus, in going back to slightly recut all films, you certainly could add in any deleted or extended material. I don't have the 'Explosive' DVD release...so I'm not sure what's out there.