Bank One Corp. president and CEO John B. McCoy is being a bit coy about his intentions for the $260 billion-asset banking company's international strategy.

The issue is crucial and raises the question of whether a company that was once regionally focused can remain almost entirely domestic when its assets go well beyond $100 billion.

That's the situation Mr. McCoy finds himself in as a result of Bank One's acquisition in October of First Chicago NBD, a money-center bank with 11 offices in 10 foreign countries.

Suddenly the banking company that put Columbus, Ohio, on the map as a powerful regional financial center, whose bread and butter was consumers and small and midsize companies, found itself headquartered in Chicago and banker to some of the world's biggest companies. Unlike Bank One, First Chicago engaged extensively in money market and international activities to serve its giant clients.

From his words it's hard to determine where Mr. McCoy will take the bank internationally. "Our major strength is our U.S. franchise, and our international strategy revolves around that franchise," Mr. McCoy told industry executives at the annual meeting of the Bankers Association for Foreign Trade here last week.

But can a huge U.S. banking company serve the nation's biggest corporations without a substantial money market operation and an overseas presence? And in today's global village can a bank work exclusively with U.S. companies and not with foreign behemoths?

Last week Mr. McCoy dismissed speculation that Bank One plans to cut back the wholesale and capital-market activities inherited from the former First Chicago, but he announced in February that Bank One would shut down its proprietary derivatives trading business in London. "We were not a major player in London," Mr. McCoy explained.

In outlining his policy, Mr. McCoy said the company will base its international banking services on its U.S. corporate customers' needs, mentioning funds transfer, trade finance, foreign exchange, and global treasury management.

Will such limited services be sufficient to retain multinational companies as customers? Maybe not. Multinational corporations often farm out such mundane but profitable business to banks that help them in more complicated and risky activities. Without the capability to satisfy these bigger needs, Bank One might be throwing away much of the value of its $30 billion investment in First Chicago.

Mr. McCoy says that in areas where Bank One has massive scale, such as credit cards, it will expand overseas. Its credit card business is tied for No. 1 with Citigroup Inc. Bank One, which had $70 billion of credit card receivables at yearend, is making a major push into credit cards in Canada and Europe, and announced plans to hire 1,600 people in both regions.

The key to succeeding globally lies in developing large volumes in a limited number of operations, Mr. McCoy said.

"We are going to be living in a global world, and it makes sense financially to be a global player," Mr. McCoy said. "But banking is a scale business, and smaller companies will fall by the wayside."

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