That is the maximum. You are allowed 2 credit cards and 1 charge card for both personal and Biz products.
I am curious, do you have 3 credit cards in any type or is the breakdown how I have described it?
There is no limit on the number of products you can carry (or the annual fees you're willing to pay). Everyone's situation is different. If you make enough and/or spend enough, Amex will work with you.
I have 7 products. 5 personal (1 charge, 4 revolving), 2 business (1 charge, 1 revolving). Each one is used for a specific purpose.