My recommendation would be to have the user that is doing the PO Receipt of Goods (or a back office person after the fact, if the warehouse is doing the PO Receipt of Goods); modify the Quantity Ordered to match the Quantity Received. Do this step before the invoice is received.
I would also recommend a PO Form that is for accounting purposes, that lists the Quantity Ordered, Quantity Received and Quantity Invoiced. I typically setup a form like this with a ""message"" that highlights discrepancies. It could be anything from just an "" * "" to spotlight a discrepancy, or a message like ""Under Received"" or ""Over Received"".
Accounting would print this PO form to review before receiving in the Invoice. If the Qty Ordered does not match the Quantity Received, that should be fixed first.
Then do the PO Receipt of Invoice to match the quantity received. That might not be the same quantity on the Vendor Invoice, but as long as the ""extend"" dollar amount matches the Vendor Invoice, you should be good. This process will properly close the line of the PO (three way match). As well as drop the line off of the PO Clearing Report.