There isn't a way to match more than one payment to a single Bill or Invoice unless both payments are needed to make up the total. 

If you create the Payment by clicking REGISTER PAYMENT and there is an overage, if you leave the PAYMENT DIFFERENCE selection of KEEP OPEN, the amount is kept 'on account' to be applied to a future Invoice/Bill.

If you create the Payment by selecting a Bill or Bills, and choosing REGISTER PAYMENT from the ACTION menu, you won't see the PAYMENT DIFFERENCE section. In this case, if there is an overage, it is also kept 'on account' to be applied to a future Invoice/Bill.

A payment in Odoo is posted as soon as the VALIDATE button is clicked, even if it isn't matched with a Bill.  

If you ever have a zero balance on the Aging for a Customer/Vendor - it happens because the amount due and owed is the same AND the corresponding payment hasn't been matched - so the net is $0.