James M. Cracchiolo's assignment at American Express Co. may seem like trying to move an elephant against its will.

Mr. Cracchiolo, president of global network services, is in charge of persuading banks to sell American Express cards. He must battle the popular perception that his company is a foe of banks. He also has to grapple with the U.S. bylaws of Visa and MasterCard that forbid member banks from issuing the American Express brand.

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