When the Medicis found out, they blackmailed Eliza and forced her to use her vampiric abilities for their own purposes.
		
		
	 
That would imply that Eliza is working for the Medici against her will. That gives me an idea for how her story will play out
She begins the story mode at the Medici tower, and Lorenzo is saying how Eliza must swear allegiance to the Medici Mafia. She reluctantly agrees and is sent on a mission to get rid of the people at Lab 8.
(vs. Peacock and Big Band)
(vs. Ms Fortune)
Eliza expresses her distaste of the Medici and she gradually starts breaking away from the Medici and doing her own thing, chasing down the skullheart.
(vs. Cerebella)
(vs. Parasoul)
(vs. Valentine)
I can imagine, somewhere along the road, she will bump into Filia and Squigly (around the time in the story where other characters fight Valentine and Double), and Samson and Leviathan, upon seeing her, quickly go on the offense and attack her.
(vs. Squigly & Filia)
After Eliza beats them, Samson references that he wants revenge for Delilah (His previous host). Eliza laughes and says, "Just be happy that I didn't kill THIS host, as well. I have more urgent matters to attend to at the moment. Eliza goes to the Catacombs. 
(vs. Marie)
Then, after the fight with the skullgirl, she approaches the skullheart. She starts laughing while thinking of the flashback of Lorenzo saying that Eliza must swear allegiance with the Medici. She proclaims that "no one can control her" and destroys the skullheart and rushes to the Medici Tower to pay her "respects" to the Mafia. 
(vs. Black Dahlia)
I haven't the slightest idea of what she would do with the skullheart though....
Any thoughts on this?