Is it possible to reenlist with an RE-4 (honorable discharge)?

With an RE4 your chances of returning to military service are near zero.

You can appeal to the Board for Correction of Naval Records if the RE-4 was in error (i.e. administrative error): otherwise it is doubtful. In 1986, as a result of an sexual battery accusation against my biological daughter (i.e. I was charge with sexually stimulating my 7 year old daughter, while both fully clothed, by rubbing her vaginal area with the nape of my neck by the City of Norfolk - no surprise here) and, via plea agreement, was force, while the case was continued, to server five years of unsupervisory probation. Though, during my subsequent divorce it was determine that my ex-wife staged the incident, the Board for Correction of Naval Records, though agreed with the finding (and my last evaluation stated this was the reason for the 2.0 rating for person misconduct though my overall evaluation rating was 3.4 - granting me the Honorable Discharge at the end of my active obligated service (no time lost)) of the dismissal, ruled the RE-4 was an "management control procedure" and stated the Honorable Discharge is proof of no misconduct while on active duty. Though I have pursued a career with the federal and two state governments (I have never been asked a question about the RE-4 during federal/state government employment) many private sector contractors have questioned about the RE-4.

Though my recommendation for anyone that has received an Navy Honorable RE-4 is to try to appeal to the Board of Correction for Naval Record, if the appeal is not granted, it is not necessary the end game - life does go on. Recommend - use the GI bill and obtain a good educational background (i.e, Undergraduate and graduate studies) and build on the positives. Learn from your mistakes (for me, find a better candidate for a second wife - it worked well the second time around), and move on looking to the future.