Yes, it is possible. With that intention, you must meet the following: the other jurisdiction made a mistake and that mistake is in your invoice and you paid the registration fees twice for just one vehicle. If you meet those, then a refund request is indeed possible.
None of your plates are lost or have been stolen, don't they?
In fact, yes. Some pair of plates of mine are lost right now.
Very well. Then you should go to a police agency and get a MV-78B form for Report of Lots or Stolen Motor Vehicles Items and once completed, send it along form IRP-6.