Well, there'll likely be intense family drama. Maybe some members want to go straight while others are deep in the criminal world. There could also be fights over leadership and struggles to keep their vampiric identities hidden while committing crimes.
The comic might feature storylines like a rival vampire group trying to take over their territory, or the family getting into trouble with vampire hunters. There could also be love triangles and conflicts over who inherits the family's criminal empire.
You can expect lots of power struggles within the family, maybe some internal betrayals, and of course, battles with other supernatural forces or humans trying to stop their criminal activities.