Erza had no other purpose in Paris than to get close to David. She even had plans to enroll at the University of Paris.
There was nothing else she could think of to do but to make David more and more fascinated to the point of being in love with her.
That way, she and David would become a couple who owned and shared everything.
At that point, she thought David would think of her welfare by giving her his blood.
However, how could she build a deeper relationship if Jane kicked her out now, when she had just met David again?
David thought Jane wouldn't mind Erza coming along if it was in a personality where she was very open-minded.
Unfortunately, she was a bit yandere now.
For this matter, he chose to keep quiet.
It was the private business of the two women.
"If you don't want to go, then we'll go down," Jane replied in a tone as if she didn't think about Erza's opinion.