always thought the max # of personal cards allowed by Chase was 4... I mean they will approve you for more than 4, esp if its auto approval. but then they might shut you down if there are any red flags or manual reviews, and they may site too many accounts etc.

biz cards should be 'unlimited' in theory, esp if you apply as a diff biz or using a diff EIN for each card etc.

and in other general terms to keep em happy: do not abuse rewards programs, do not MS, do not buy GCs etc.