After the initial claim is denied, one can apply for reconsideration. The reconsideration is almost always is also denied. The reason for this is that the same office that denied the initial claim then reviews the case a few weeks later for reconsideration. It would be silly to award benefits in a case that was denied only weeks earlier. For this reason upwards of 90% of cases are denied at reconsideration stage.
A claimant has the best chance when appearing before a judge on appeal. Social Security Disability and supplemental security income benefit claims that are denied at the Initial level will almost always need to be heard by an Administrative Law judge before they can be approved. Once the initial claim is denied only appearing before an administrative law judge can win the case.