American Express regards the individual as the applicant, not the business. (You must provide your Social Security number on the application, even if you also provide a EIN.) Therefore, if you have had the same card before you will be able to open it again, but not to receive a bonus unless you you receive a targeted offer without the exclusion.
Yes this is what I meant. I also meant that if OP had a partner in business, partner could open up business card using EIN of company.