Yes, you can. However, it is unlikely a further refund will be determined.
When you accept an offer, it is usually a full and final settlement of the matter. If it is established this has occurred, it is unlikely a further refund would be awarded to you.
If you have been made an offer but find it unsatisfactory, you should decline that offer and lodge a complaint with ATIA.
Even if you’ve received a refund, ATIA may investigate other aspects of your complaint that relate to the ATAS Code of Conduct.