Hi Mellina
One option is to apply the $60 payment from the Customer against the invoice to the Customer leaving $240 outstanding on that invoice.
Create a Charge (say) "Government Contribution" pointing a to a clearing account in the balance sheet
Then take up the payment of $240 from the "Gov" BP and put it to the Charge and enter some useful information in the description so you know which Customer BP the receipt relates to.
Go back to the Payment Allocation Window and select the Customer and then select the the invoice which will say $300 and open $240 ... then select the Charge "Government Contribution" and process.
[It would help if there was a new field called "Description" which carried through to the GL posting of the Payment Allocation so you could put information to allow you to easily reconcile the GL account linked to the Charge "Government Contribution"]
The above would keep all the accounting correct but whether it was a practical solution may depend on volume of transactions.
There is a downside to to not directly linking the Invoice BP to the Payment BP. At present you can use the Automatic Account Reconciliation to reconcile AR Control Account(s) and create a report which shows the amount outstanding for each BP for each AR Control account and it lets you see which invoices make up the balance. If you allow an invoice from BP1 to be cleared by a payment from BP2 then you would lose that capability. In fact I do not see how you could prove to an auditor what made up the balance of the AR Control Account particularly if you had multiple AR Control Accounts.
regards