Itachi from Naruto is an EII villain, but as the story unfolds you actually just see hes a character capable of doing greatly horrific things to protect what he holds as more important (his baby bro). Ultimately he's a a neutral character capable of such honorable good deeds its almost unworldly, and just makes himself look like the bad guy to preserve the good hes done

EII and villain arent contradictory imo, they just dont make for as interesting of a villain in a novel format.