Does anyone make two different car rental bookings so they have a backup?

I’ve booked a rental car in Japan for next year. I ended up going with a local rental company because it was quite a bit cheaper than the big name car rental places. They have good reviews, but I still worry a bit about renting from a small company and because it would seriously mess up our plans if we didn’t have a car. So, I was thinking to make a second booking with one of the larger car rental companies as a backup. Any problems with doing this?