Shortest path is to copy the invoice and add a single payment or reduce the price of items. Otherwise there’s no functionality for this case.
Keep in mind that this will lead to wrong statistics because of the duplicates.
You create a new invoice for the same cause, not? E.g. you bill 2 hours, customer pays 1, you create a new invoice for the unpaid amount. In the system you have now 3 total billed hours instead of 2. Or did I misinterpret something?