I'm in the middle of writing a book where the protagonist is a narcissistic psychopath, and while I personally am having a lot of fun with it and hope I'm doing it well enough, I understand this is a difficult feat to do without alienating the reader. So I was hoping to create this question as a repository of ideas people in this stack exchange have on how to write a compelling psychopathic protagonist.

Here are the ideas I myself used:

• She's utterly vindictive and selfish, but through sheer happenstance, usually ends up screwing over people even worse than her (in her case, mob bosses, slavers, and bourgeoisie).
• She has a set of principles which, while not ordinary, demonstrate she has standards (for instance, she despises the concept of slavery because she considers forced collaboration to undermine the selfishness of both the slaves and the slavers).
• She's got relateable struggles exacerbated by her mental illness (in her case, extreme loneliness from regular social faux pas, usually her fault, sometimes not).
• Her narcissism is sometimes outright humorous in its extent, with her often missing the point in an endearing way.
• The story has sympathetic side characters that give the reader people to root for even while rooting for her eventual downfall (like her sidekick, a self-esteem-free boy who she's using to feed her ego and assist with his powerful magic).
• Her arc is the tale of someone going from an exiled noblewoman with nothing to her name, to nutty wildcard, to legitimate and terrifying threat, making her a villain protagonist by the end with sympathetic, heroic antagonists.

However I know there's multiple ways to go about making a narcissistic psychopath protagonist work. As stated, I'd like this question to be an idea repository for others rather than strictly a solution to my problems. So, what are you guys' thoughts?