8 Milestones in the Evolution of Owen Wilson
You, Me and Dupree (2006)
...though not in You, Me and Dupree. In the aimless comedy, Wilson played the wacky part of a romantic comedy "love triangle," as the loner house guest who comes between his best friend and his friend's new wife. It didn't really work. Wilson would go back to regular rom-com grounds with the $140 million grossing Marley & Me, and now How Do You Know.
Darjeeling Limited (2007)
Just two months after the actor's alleged suicide attempt, this 2007 Wes Anderson film (which, for a change of pace, was not co-written by Wilson) was released. Like in Bottle Rocket, Wilson straddled the line between conniving and dippy, this time herding his two brothers (Adrien Brody, Jason Schwartzman) on a soul-searching trip through India to reconnect with their mother (Angelica Huston). Eerily, Wilson's character spent most of the film in facial bandages, which when removed during a later scene, revealed bruising from an accident that may or may not have been a suicide attempt.

Comments
I'd add 'Minus Man' as an interesting and significant point early in Wilson's career.