My own preference, if you want to use Two-Face extensively, is to make his post-scarring plans and goals "To take the crime he once fought as District Attorney, and rule it". He wants to become the Kingpin, basically, both to indulge his own desires that he used to forgo as a law abiding part of the city's government, and as retribution against the criminal establishment that he always hated and still does. If honesty and integrity just leaves you scarred and left for dead, then its time for violence, corruption, and fear.
Which yes, would mean that being taken over by Two-Face is a rather fraught position for a gangster. Your boss is mentally unstable, and he hates you. Unfortunately, Two-Face is actually really good at what he does, both due to being essentially an Evil Action Hero, and also an entire career learning how organized crime works and accumulating information about it and its corruption most of which he couldn't quite use before, because of laws.