New Game+ is an extension to Oxenfree released on May 31, 2016, including new dialogue, events, and endings.
New Game+ is accessed after having beaten the game once. The player will be presented with a new option on the main menu labeled "Continue Timeline?", which will trigger a new save with the New Game+ content.
Sean Krankel on "Possesses PS4 on May 31 with a Host of New Features" post on PlayStation Blog:
I’m gonna try to do this without getting all spoilery. When you ________ the game the first time and come back to the game anew, Alex will have different, déjà vu tinged dialogue choices. Suddenly you realize that Alex is ________, and now you must ________ if you want to see tomorrow.
Kevin Riach on "New Game Plus Update is Now Available" announcement on Steam:
LEAVE. IS. POSSIBLE.
That's right everyone, today is the day! Oxenfree's NewGame+ content is out now to all players for free. Every owner of the game should now be able to update Oxenfree and experience the continuation of Alex's story. The new mode will allow players to continue beyond the original “ending” into a new and exciting chapter of the game's story. We are incredibly excited to share all of this new content with you today, and can't wait to see what everyone thinks!