Absolutely you can do this.
Create a Group, Share your story map with the Group.
Invite other authors to the Group.
To make changes, the other members of the group have to have a user role that gives them adequate power - in our organization this is frequently a Publisher role, but ESRI has a new "StoryTeller" role that looks interesting:
Storyteller User Type | Bring Storytelling to Your Organization
Jay
Jay
Washoe County GIS