No easy answer. Depends on a wide range of things, such as income, credit score, utilization rate, debt to income ratio... I know people with 10+ active credit cards, perfect credit scores and can get any card they want.

Your ideal benefits should inform your card strategy. Depending on what you want to do you may find that you don't need 10+ cards at once.

So to be more helpful, it'd be good to know what you hope to accomplish...