Yes – you’ll bring a lot of bargaining power to the table if you’ve been a long-time customer of your chosen lender. They’ll want to keep you on as a customer across the board and not lose your business to a competitor, so they’ll usually be willing to negotiate. You don’t have to have been a long-time customer to negotiate a better deal, though; lenders know that they’re in a cutthroat industry and will usually be very keen to accommodate you.