How does owning multiple CCs affect one's credit score in the US?

I am based in Germany and I have to hold myself back from applying for multiple cards, since the more CCs you own here, the lower your credit score will be. The logic behind it is quite simple: they multiple limits on all your CCs and if this number outweighs your monthly income, your score goes down (even if you have paid all your previous bills on time).

Does the same logic apply in States?