The Gemini's spiritual "master", who had possessed the girl Regan MacNeil, was furious at being pushed out of the child's body and is exacting its revenge by putting the soul of the Gemini Killer into the body of Father Karras. Each evening, the soul of the Gemini leaves the body of Karras and possesses the elderly people with senile dementia elsewhere in the hospital and uses them to commit the murders.

Source Wiki. Writer's subplots.

Quote: "The Gemini's spiritual "master", who had possessed the girl Regan MacNeil, was furious at being pushed out of the child's body and is exacting its revenge by putting the soul of the Gemini Killer into the body of Father Karras. Each evening, the soul of the Gemini leaves the body of Karras and possesses the elderly people with senile dementia elsewhere in the hospital and uses them to commit the murders."

Source Wiki. Writer's subplots.