I once rented a car in NY from Hertz and drove to Montreal. Because it was a US-based origination, they had to use some sort of manual slip to add the additional driver. Because it never went through the computer system there was no charge. Probably wouldn't work for the same country, but I just found it an interesting nuance of Hertz's system. If you wanted to try, you could rent initially without the additional driver and then stop at another location to have them add them to see if it "falls through the cracks".

As bhomburg pointed out, you should be able to remove the additional driver after the fact, but don't necessarily count on the counter agent being able to figure that process out. It's not something they do every day, and of course YMMV depending on company.

All of that said, if you are renting in the US, you might consider renting using the Costco, AARP, AAA, USAA discount codes as all of them alloow for an additional driver.