Can I extend my J-1 status beyond seven years?

Maybe, but you may not want to do so if you are considering applying for a J-1 waiver in the future.

Under the U.S. Code of Federal Regulations (22 C.F.R. 62.27(e)(2)), the duration of a foreign physician's participation in a program of graduate medical education or training is limited to seven years, unless the physician has demonstrated that the country to which he or she will return has an exceptional need for an individual with such additional qualification. See also 22 C.F.R. 62.43(c). The Department of State requires a letter of "exceptional need" from the physician's home country.

Even if you are eligible for a J-1 extension beyond the seven year limit, you may not want to pursue it. If the extension is approved on the basis of an exceptional need in the home country, the Department of State notes that the approval will weigh heavily in any future consideration of a J-1 waiver. The policy reason is clear; if your home country has an "exceptional need" for your talents, the U.S. government will want you to return to your country to fill that need.

As a result, if you plan to apply for a J-1 waiver eventually, a J-1 extension beyond the seven year maximum will likely be a bad course of action.