Without knowing your specific situation, generally, you can reenlist before your extension starts. However, you need to check with your CCC to verify if you are eligible. Since PTS is based on Soft EAOS, you may need PTS approval before reenlisting.
NAVADMIN 352/10: PERFORM TO SERVE - FLEET RATING IDENTIFICATION ENGINE INTEGRATION POLICIES AND PROCEDURES (SPECIAL CIRCUMSTANCE APPLICATIONS MAY BE SUBMITTED REGARDLESS OF SEAOS, BASED ON PRD FOR SAILORS REQUIRING TO OBLISERV FOR ORDERS, END OF ACTIVE OBLIGATED SERVICE (EAOS) FOR SELECTIVE REENLISTMENT BONUS (SRB), OR
OTHER SPECIAL CIRCUMSTANCES REQUIRING ADDITIONAL OBLIGATED SERVICE.
*MILPERSMAN 1160-040 When a member reenlists. The extension(s)shall be canceled as of the date of reenlistment, provided term of the new enlistment exceeds the total aggregate months of extension(s) to be cancelled.