The Bourne trilogy has been been extremely popular and profitable for Universal and is one of the bright spots in their financial ledger. As pointed out by /Film, the trilogy has grossed over $945 million worldwide with the last movie, The Bourne Ultimatum responsible for about half that total.
The existing three films have exhausted the original source material - novels written by Robert Ludlum, but there are two additional stories that have been penned by Eric Van Lustbader (how's that for a cool name?): The Bourne Legacy , and The Bourne Betrayal. Unfortunately if you head on over to Amazon.com you'll find a lower opinion of the non-Ludlum novels than of the original three.
I think that just because the later novels are weaker that doesn't necessarily mean the screenplays won't be good. Just as it's possible to take amazing source material and destroy it on the big screen, I think an excellent writer could take a weak story and turn it into a great film.
Both director Paul Greengrass and Matt Damon have committed to returning for a fourth Bourne film despite both having said they're done with the series.
Source: Variety via /Film