Approval Rules: Bank of America is unlikely to approve a new credit card if you currently have more than five open Bank of America credit cards. Additionally, according to the 2/6 Rule, Bank of America generally does not approve new credit card applications if you have opened more than two credit cards from any issuer in the past 12 months. However, this limit is relaxed to six cards in the past 12 months if you hold a Bank of America bank account. For the Bank AmeriCard, you may be ineligible for a new card if you currently have, or have had, the Bank AmeriCard within the past 24 months, as eligibility typically requires the previous card to be closed for a full 24 months.