I've used it broadly to refer to the object egoist wanting a subject egoist who was successful and showed her worth.
I've had one straight and some gay patients who were very clearly looking for a romantic partner who was exactly the same as them.
However, I have also had a patient who was with a sociopath. She told him she wanted him to leave and he stole some of her things and he threatened to put her naked pictures online and she called the police on him to no avail.
she described him as a sociopath, that he doesn't care about others, that he's threatened the police and is lawless or above the law, that prison is like a vacation for him, that he'd break any restraining order... he also cheated on her many times and was attractive to women and viewed as strong.
It took me a while to place it but my patient had often referred to her wild days in the past and how she didn't care for others either. She broke homes, took what she wanted, and was quite lawless herself.
At some point she became anxiety ridden, isolated in her home, and while small chances for her to move on came up that she didn't take I knew she needed him in some way. I analyzed it based upon her echoism and fear of starting her own life, I analyzed it based upon her narcissism and preferring to imagine having the perfect life rather than attempting to actually attempt to have a real life, and though these were part of the situation I think that the narcissistic object choice in which her boyfriend represented the wild, sexually desirable, selfish, and uncaring part of herself seemed to have the most weight for her. If memory serves me correctly her response was "that is gross" and that it felt right and was 'disgusting' to think about and a surprise.
No longer having this part of her personality operating means that the function is different than the second examples of people who want to have romantic partners who are just like them because their drives are still functioning. My patient ejected a part of herself and wasn't functioning in many active ways.
Additionally, her staying in the house also seemed very significant to me because of what I've come to understand about the volar father-substitute. I wish I would have asked her to talk about the house itself.
I'm loathe to call this projective identification because as I've understood Klein to use it, it seems to be about taking the place of the parental imago and putting one's anxiety or ego ideal tensions into the other person.
So, maybe narcissistic object choice is the way to go here...