I am working in Germany with a visa type which is green card equivalent of green card. As a principle changing employer is allowed. Now I am changing job but with another title but on my permit it say i can only work as software engineer. I just sent an e-mail to foreigner's office to just to get information and suddenly they gave me an appointment to solve the problem, they will just modify my permit. They are encouraging you to change employers and vitalise the economy. And foreigners are welcomed here because they have talent, not because they are cheaper. We are treated same as German citizens. Comparing to the US policy, it is 3 times better i think.