THE IDENTITY OF YOUR NEW business competitor across town may surprise you. It may turn out to be a lawyer -- your own lawyer -- who is trying to take your customers away.

Working with clients on legal problems is still their major concern, but a dozen or more law firms have opened subsidiary businesses, and the trend promises to spread. "If lawyers don't seize the potential the business world offers, they're missing a big opportunity," says Leonard Schaeffer, the managing partner at Pechner, Dorfman, Wolffe, Rounick & Cabot, in Philadelphia. But the new ventures raise serious ethical questions in the legal and business worlds.

Most lawyers are entering businesses that complement their clients' needs. A Philadelphia firm specializing in labor law, for instance, recently acquired a consulting company that specializes in labor relations. An Arizona firm opened its own advertising agency. Firms in Memphis and Atlanta have entered investment banking. A Washington, D.C., firm opened a financial consulting service, and a Los Angeles firm set up a real estate brokerage company.

Attorneys claim there aren't enough of those princely $200-per-hour fees to go around, so they have to venture beyond their profession for growth. President Reagan's deregulation stance dried up some business; so too has the trend among large corporations to pare costs by doing more of their legal work-in-house. All those cutbacks have come at a time of explosive growth in the number of licensed attorneys, up about 25% since 1980.

Conflict-of-interest problems may plague the new ventures. If part of a law firm is working on a real estate deal, legal scholars question whether another part can advise the same client about legal difficulties with the deal. And clients are likely to worry that confidential information about their companies could be used by a firm to aid its own subsidiary. "Any time that a law firm's client has any business relationship with that firm's nonlegal business, I see a red flag," says New York University Law School professor Stephen Gillers. "Many firms are doing this with the best of intentions -- but you can fall into ethical traps even when you're on the side of the angels."