If my exchange program ends in 4 months, can I extend my J-1 visa for the next year participating in a different exchange program?

Hello.  This is the sort of legal problem for which I recommend that you seek private counsel; it would be inappropriate to state a specific answer to your posed question. I myself would need to confer with you in detail about your unique fact pattern and your desires.  In the event that the general answer for your personal situation is 'no', please realize that it is possible that exceptions to general rules certainly may be made for special situations, and having a private attorney assist you likely will be of immense help to you in my view.  A J-Waiver exists as a possibility in certain circumstances. Please seek out a qualified private attorney to assist you in seeking your goals.  I recommend that you telephone several attorneys in choosing, because it is very important that you feel comfortable with the attorney you select to help you at this time.  All the best to you.