How can I have a new dropdown for each entity reference added?
I would look into the Chosen and/or Select 2 modules. They both work to improve UX for select fields.
I've used the Chosen module multiple times in the past, so that's where I'd lean here. The module improves the UX for users managing multiple selections on a select field. The chosen library alters the UI to allow users to easily select multiple options - it even provides autocomplete functionality to limit the results of the select field.