If you have no other lines of credit (student loans, car payment, mortgage, etc) then you definitely will need more than one credit card. Your credit score is a great indicator, but unfortunately is separate from your credit "strength". Open a new credit card if you can, and also increase the credit limit on your existing card if it is low. I had the exact same issue. 780 credit score but had to have my dad cosign on an apartment. Make sure the cards you open have no annual fee, preferably have a good sign on bonus, and make sure to set them to autopay the full balance each month.