You can now record partial payments for invoices in "Payment Due" state using the "Record Payment" option.
While recording the payment, enter the partial amount collected in the "Amount Received" field.
Say, your customers only pay half the amount now and pay the rest later, you can record the partial amount being paid now and that is deducted from the total amount of the due invoice.
The invoice remains in "Payment Due" state until the full amount is recorded.