One of the most compelling parts of Carol Emshwiller's "I Live With You" is figuring out who and what the narrator is. I would argue that the narrator is Nora's split personality. This would certainly make the story a "Diverse Position."
I do not know a lot about split personalities and how accurate this would be as a portrayal of the condition. However it seems to me that this other person was created to get Nora out of her rut. It makes her act and live in ways that she would not have otherwise. It's a mischievous force, but not a malevolent one. I would argue this other personality is created by Nora's subconscious mind as an act of rebellion against her social anxiety and reclusiveness.
As the story progresses, Nora starts to live with the personality, accepting some of it. At the same time the narrator starts to refer to Nora's possessions as hers: "Our credit card" for example. Then, at the end of the story, after Nora has changes and doesn't need the other personality anymore, the personality leaves, and says "your credit card and keys."
At the end the narrator says that Nora will lock her up with "your old mousey clothes." This seems to suggest that the narrator will be forced to take on Nora's old personality, furthering the idea that she has to be the other half of Nora, so she leaves.
If the story is read with this in mind it seems that the story gives insight into a state of being not typically explored in literature. Split personalities usefully crop up in crime dramas where the killer didn't know they were the killer when they were questioned or whatever. This shows this perspective in a new light. It is portrayed as helpful to Nora, giving her a life where she would have otherwise withered away her existence on TV dinners and solitude. Altogether it is a unique way of looking at a unique position.