The one-room office of Donald J. Tomaso Associates, in an aging building on the fringe of Chicago's La Salle Street financial district, has three battered desks, one typewriter and a jumble of card files. From that dingy setting, Donald Tomaso, 36, handles some of the biggest stock deals in the U.S. Often talking simultaneously over two telephonesone connected to a buyer, the other to a sellerTomaso arranges direct trades between large institutional investors. He is one of the handful of entrepreneurs who run the "fourth market," so named because it bypasses the three more conventional methods of trading securities:...

