Changes to Sales Order

Once a Sales Order is created, ship confirmed, and interfaced to AR to create an invoice can it's(Sales Order) price/quantity ever be changed?

We have a new business process where once the Invoice is issues, the customer comes back with a different amount for the invoice and this change in the invoice amount should also get back to the  SO on which this invoice is based. I looked at various profile options and setups but did not come across any that are of help in this scenario.