If you get a waiver maybe.
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Depends in facts not posted, but odds are NOzt in your favor. See your recruiter, he or she knows far more about your reenlist meant options.
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The RE 3 code would require a waiver to reenlist. The fact that there is a military drawdown under way your chance of reenlistment is low. If military service is a priority then you may consider trying to petition for an upgrade on your RE code with the applicable military discharge board.