The Bourne Legacy (2012) without any perceptible Matt Damon is nontheless pure, distilled Bourne.
It starts with Jeremy Renner as the new Bourne-type agent, swimming bare-assed in a frozen mountain lake. He is racing solo up through mountains, snow and wolves. This is my favorite part - just awesome scenery and physical activity. It reminds me a lot of the start of Hanna, a movie with a similar plot - super-agent vs. the agency that built her.
Because while Renner is on his Outward Bound expedition, several Shadowy Government Agencies are shutting down Project Codename with extreme prejudice, killing everyone involved as showily as possibly (to keep it quiet). That includes a drone with a Hellfire missile with Renner's name on it.
In order to stay super-powered, the Renner-class agents need to take drugs they call chems. So Renner needs to get more chems as well as dodging the government kill-squads. He heads to the labs where they have been processing his bloodwork and kidnaps/rescues scientist Rachel Weisz. They fight, travel to Manila, and fall in love.
Renner is way different from Damon's Bourne. The first time he opens his mouth, he comes across as a kind of amiable Minnesota-born surf bum, or like, you know, whatever. He gets to do grim and determine, of course, but has a kind of lumpy-faced average guy charm that makes him look pretty natural sucking on a beer.
Even though this is not part of the official Bourniverse, it has a very Ludlumesqe quality, with lots of "sitrep" and "delivery systems" and "weapon platform" type dialog. Along with all the project codenames, this made the plot pretty hard to follow - except that it isn't hard to follow, because we know the routine. Also, we love the routine: unrelenting action.
In conclusion, we would watch a trilogy of these new Bournes, but I don't think they will get made.