tl;dr
You can use the concept of the Furies, the Muses, and the Humors to create rich and deeply flawed characters.
The Three Furies
When talking about character, we often talk of their core wound which is the thing from which they need to heal.
- Alecto
- Megaera
- Tisiphone
The Four Humors
They map to bodily fluids and the elements, but like the zodiac. This is a base temperament, and one that set the reptilian response for a character.
Yes, I know that this isn't technically Greek, but it fits the concept.
- Sanguine
- Choleric
- Melancholic
- Phlegamic
The Nine Muses
They map to what the character wants or gets inspiration from. It's not a direct mapping to their "want", but it helps shape it.
- Calliope
- Clio
- Erato
- Euterpe
- Melpomene
- Polyhymnia
- Terpsichore
- Thalia
- Urania