Unfortunately, there is no way to adjust either a full refund or partial refund after the fact – you can only refund an order once.
If you need to increase the amount that was refunded to the customer, we would suggest giving them a promo code for the incremental amount. That is, if you refunded $15, but you really needed to refund $20, you can create a $5 promo code and assign it to the customer’s email address. Please see our How to Create a Promo Code post for details.
Hope this helps!