For companies tangling with regulators, huge fines may soon be the least of their worries.

The U.S. Securities and Exchange Commission is divided over whether it should impose severe restrictions on banks and their executives who break securities rules. For top executives, those punishments could include a lifetime ban from working at publicly traded companies. And some at the Commission are advocating greater use of “bad actor” bars against financial firms found to have committed misconduct, which would impose strict limitations...