When you say the counseling came back I am assuming that someone senior in the chain of command found the counseling to be substandard or felt that certain items were not properly addressed.
You can rewrite the counseling and ask the Soldier to sign, provided the chain of command supports your action. I would run the corrected counseling by the chain of command before you attempt to counsel the Soldier again.
You can rewrite the counseling statement and simply put a notice on the new counseling, “This counseling modifies the counseling you received on _____,” or “This counseling documents the verbal counseling you received on ______.” Once you have completed the new counseling, allow the leader who disapproved the previous version to review the changes prior to sitting down with the Soldier. You should also keep a copy of the previous counseling attached to the new counseling in case there are ever any questions as to why the counseling was rewritten.