When the bell rings to mark the opening of trading on the New York Stock Exchange each morning, brokers wanting to buy or sell American Express Co. shares swarm around James J. Maguire Jr. That's because he's the only person on this crowded, noisy floor of a building that's come to symbolize the U.S. stock market who is designated to handle trades in the shares of this multinational financial conglomerate.

In a speech tonight, Securities and Exchange Commission Chairman Arthur Levitt Jr. is expected to lay out a framework that could jolt this clubby world and perhaps radically change the way U.S. stocks are bought and sold. He is expected to lay out a list of options that includes allowing Wall Street's biggest firms to trade certain stocks that heretofore could only be traded on the NYSE when that market was open. He is also expected to suggest that one self-regulatory body could police trading activity across all stock markets.

"This is a historic moment in market structure, because [the SEC] could decide to keep the market structure as it is and not tackle some of the anti-competitive structures that exist. . . . Or Levitt could announce a series of changes that would allow innovation and competition within a framework of investor protection," said Carrie Dwyer, executive vice president of Charles Schwab Corp., the discount and online brokerage.

"If Levitt opts to continue allowing competition to flourish, customers who have already seen costs falling enormously," could benefit from further lower prices, said Dwyer.

The NYSE is expected to oppose several of the suggested changes and will likely fight to keep its monopoly over lucrative trading in many of the nation's blue-chip stocks. Several new trading networks--called electronic communications networks--which have sprung up to satisfy investors who want to keep trading outside the Big Board's 9:30 a.m.-4 p.m. hours--are pushing for even more changes so they would have the chance to compete more effectively for orders. Major investment banks are also pushing for regulatory changes as they try to cut all unnecessary costs and increase their global competitiveness.

If the SEC decides to open up the securities markets to more competition, it could result in lower trading costs and pave the way for a host of new services, such as evening trading, supporters say. Others fear that the moves could fragment the centralized marketplace.

Among the issues that policymakers face:

* Should the NYSE and the Nasdaq Stock Market be allowed to "demutualize?"--that is, change their status from membership organizations to for-profit entities run by shareholders.

* Who should regulate the for-profit organizations? Currently NYSE and Nasdaq are allowed to regulate themselves. Their regulatory operations are overseen by the SEC. The SEC must decide if that still makes sense.

* How should the newcomer trading networks be regulated?

* Should evening trading be encouraged?