How does the blue card work? Is it only valid as long as you work for the employer that sponsored you to get it? Can you change employers after some amount of time and still retain it?
Whenever I got mine, the person at the Ausländerbehörde said that the card was tied to my job title, not employer.
To get a blue card you primarily need an unlimited contract. Companies do help with the process of procurement, like setting up an appointment. Once you get your blue card you also get another "green slip" that mentions your current employer along with your job role. Anytime you move to a different job, this slip needs to be updated, which is then done by your new employer.