I don't know. I'm scared to say "he can't do it", then he turns out to be the next Matt Damon/bad ass (more on him later). I also don't want to say "that's a great idea" because Renner is yet to carry a film on his own. His biggest part obviously came in The Hurt Locker, but he wasn't the main attraction there. Here's what Renner had to say about the rumor that he's taking over the franchise:
It’s a franchise to potentially take over… I can’t predict the future and what they want, but that’s certainly the idea.