The council was set up by the Dodd-Frank Act and is made up of virtually all the federal government’s financial regulators. It is authorized to use such criteria as size, interconnectedness and “mix of activities” to decide whether, in effect, a nonbank financial institution is too big to fail.

The legislation already specifies that all banks or bank holding companies with assets of more than $50 billion are automatically included in this category, but the FSOC now must decide what other financial institutions—insurance companies, financial holding companies, securities firms, finance companies, hedge funds and private equity firms, among others—are also dangers to the financial system’s stability. Under the terms of Dodd-Frank, if firms are designated as potential sources of “instability,” they will be subject to “stringent” regulation by the Federal Reserve.

Dodd-Frank has already done enough damage by identifying the very largest banks as too big to fail. This newspaper recently reported that these banks pay 78 basis points less for their funds than their smaller rivals. Adding nonbank financial institutions to the too-big-to-fail list will have devastating effects on competitive conditions in other industries. The situation is serious enough that if the FSOC goes ahead with this process Congress should consider intervening—by repealing the section of Dodd-Frank that provides the council with its authority to determine which institutions might cause “instability,” or denying it the funds to continue this part of its work.

The identification of firms as too big to fail is a mad policy: It will signal to the world, removing all doubt, that the government will take steps to prevent the failure of these firms, giving them advantages in the marketplace. If the funding advantages that have already appeared in banking are spread to other industries, large companies will be put in a position to drive smaller rivals out of business.

We’ve seen this movie before. Because of their perceived government backing, Fannie Mae and Freddie Mac were able to borrow funds at rates that enabled them to drive all competition from the secondary mortgage market.

Insurance is an example of what might occur elsewhere. This is a highly competitive industry today, with many small and midsize property and casualty firms competing effectively with the largest companies. Imagine what the industry will look like if the FSOC declares three or four insurers or their holding companies to be too big to fail and subjects them to special regulation by the Fed. Creditors and customers will come to feel more secure working with them than with others, seriously distorting competition in the insurance market. The same insidious process will occur in every other market where the FSOC declares one or more companies a danger to stability if they fail.

Some will argue that the Fed’s stringent regulation will actually be so costly to these large companies that they will get no benefit from the designation as too big to fail. Indeed, from all indications large companies are busily making presentations to the FSOC, arguing that they are not too big to fail—certainly an indication that they do not believe that there are any advantages in the designation.

Unfortunately, that’s not much comfort. If these firms are correct—if the added regulation is actually more costly than the funding advantages—things would be even worse.

Assume that Fed regulation is so stringent that the costs are greater than the funding advantages. Where are we then? We’ll have large, well-funded companies in every financial industry that are gradually losing the competitive race to unregulated or lightly regulated competitors. In the end, these large companies will have to be rescued by the taxpayers (think General Motors and Chrysler) in order to save their jobs.

The government will inject new capital, engage new managements and promise that these new managements will be innovative, efficient and productive. Then these newly invigorated companies will be set to work competing with the smaller but nimble rivals who nearly drove them out of business. Does this make any sense?

There is no compromise solution to the problem created by Dodd-Frank. Either the process of designating firms as too big to fail stops with the banking industry, or competition in the entire U.S. financial system will be substantially transformed for the worse. Once nonbank firms are declared to be too big to fail, there will be no opportunity for a do-over.

Mr. Wallison is a senior fellow at the American Enterprise Institute.