Not guaranteeing that it works, but so far a few times successful.
Steps I toke:
Rented with
www.xrentalcars.com(The rates are prepaid)
After rental period (e.g. 1 week), you ask if you could keep it for another week.
They should say, something like. Okay, you will pay that same amount again after the rental.
Upon returning the car, when handing back the car keys, just casually inform that all is okay, mentioning that you kept the car clean and no crashes.
Normally when they glance at their pc they, will just see that it's a prepaid rate and no longer will you need to pay.