Well, you most certainly cannot have 2 premier accounts even you have different bank accounts. Paypal is explicitly clear on the point that you can have only 1 Personal and 1 Business or Premier account only. Each account that you have must be attached to different bank accounts which can be from the same bank. Just a note, if one of your account is limited, you should work towards lifting the limits rather than to start opening up new accounts because they would certainly catch up with you. It is not good to cover one mistake with yet another because it just would make the matter worst for you.
If it lets you add it. If I try to add a bank account or credit card to more than one account of any type, I get an error.
You can't add a CC for 2 paypal accounts at the same time... You must remove it,The add to another account