If your Social Security disability or SSI disability claim is denied by an administrative law judge after the disability hearing, you might be able to get a second hearing by requesting that the judge's decision be reviewed. You do this by filing a request for review of the administrative law judge's decision. This type of appeal involves the Appeals Council, a body that reviews the decisions of administrative law judges.
Cases that are reviewed by the Appeals Council may potentially be sent back for a second disability hearing, otherwise known as a "remand." Second hearings of this type, or remanded hearings, typically occur when fault can be found with the decision of the ALJ (either a technical error or a more substantial error regarding the evaluation of medical evidence).
Of course, you can also file a brand new claim for SSI or SSDI benefits and, assuming your case is turned down again at the initial and reconsideration appeal levels, request another ALJ hearing. When should you seek a remanded second hearing (via an appeal to the Appeals Council) rather than trying to get a second hearing simply by starting all over again with a new application? Well, your chances of getting a second ALJ hearing are fairly slim: only 22% of cases that are appealed to the Appeals Council get remanded to the ALJ for another hearing. A disability attorney will only seek a remand when it's plain (at least to the attorney) that the judge erred in some way.
For more information on filing a request for Review with the Appeals Council and getting a remanded hearing, see our article on appealing a disability denial to the Appeals Council.