Having too many accounts does hurt your score some even if you don't carry balances but it's marginal, might mean the difference between a 790 vs an 810. I started my career as an underwriter and dealt with 100s and 100s ofcreditreports. There is also the fraud/identify theft issue that more accounts are hard to keep track of. Some of those store specific card deals hard to ignore though. If you shop regularly at BJs as part of your food shopping and will continue to do so in the future probably not a bad deal. There is no set number as it relates to quantity of accounts but I'd say it's around 5 or 6 as the cut off that begins to hurt the score. On ironic side having only 1-3 hurts your score as well.