I would definitely recommend Sam Staggs' book, "All About 'All About Eve'".
According to Staggs research and interpretation, Eve can be interpreted as a covert, "killer lesbian", as based upon the very negative, homophobic mindset of the time. Staggs uses many examples, including the following:
1)Eve's manly appearance in her first flashback scene (e.g. the masculine raincoat and hat as she waits by the stage door)accompanied by a rather deeply-voiced call-out to Karen ("Mrs. Richards").
2)Eve's attempt at making a rather agressive pass at Bill in Margo's dressing room to which he responds with a line expressing that when he likes a woman he wants to do the pursuing, not be pursued (the subtext being that Eve doesn't fit within accepted gender roles). Bill also referred to her as "Junior" in a previous scene".
3)The scene in which Eve phones Lloyd urgently from her rooming house late at night, hangs up, smiles conspiratorially with another woman sitting nearby,and walks back upstairs, arm-in-arm with her (both of whom are wearing bathrobes). There is the possible implication that they are sleeping together.
4)Upon revealing her plans to marry Lloyd, the always fey Addison compares her to him, saying that neither one knows how to love (possibly meaning specifically heterosexual love) and threatens to expose her for the fraud that she is (i.e. a lesbian, not just her made-up story of her dead war-hero boyfriend). Addison also refers to her as "killer", seemingly within the context of describing a manly prize fighter, which really hits a raw nerve for Eve.
Now, I should emphasize that the examples above and the whole idea of Eve as a cold, ruthless lesbian who steals other women's men only to further her own career are a matter of speculation.
Staggs does present very convincing arguments, to which I have not done justice in this post. I believe that even Mankiewicz is quoted in Staggs' book as having said in an old interview that the lesbian subtext has its merits.