Well, being a somewhat anal retentive person, I decided I really wanted all the doors to have the same key, and I had wanted to change all the locks anyway, for the sake of security. Also, one of the back doors didn't have a deadbolt on it, so I wanted one put on. The handyman said he could do all that, and by the end of the afternoon, all the locks had been changed to have the same key, and there was a new deadbolt on the back door.
The standard pin tumbler lock like my doors have is a piece of 6000-year-old technology. The Ancient Egyptians used it. Inside, it has a set of plugs and a rotating cylinder. When the correct key is inserted, the plugs are raised to the correct levels so that the cylinder is no longer blocked from rotating, and you can open the door. To re-key a door lock, you don't have to replace the entire deadbolt or door handle. You just have to remove the hardware from the door and replace the little cylinder with one designed to work with a different key.
Actually, I wonder how many unique keys there can possibly be with this design. I suppose the correct height of the pins can be changed in infinitesimal increments, but in reality, the increments is probably limited by the manufacturing tools, so there must be a finite number of possible keys.
The locks on my doors aren't particularly old-fashioned or charming. In fact, the doors themselves are all new, which is explains the new hardware. It would have been more fun if they looked something like this one from the Victoria and Albert Museum in London:
A few years ago, when I was traveling in London, I visited the Victoria & Albert Museum. Officially a "museum of decorative arts and design", it really comes across as a museum of random old stuff. It has collections of old clothing, musical instruments, furniture, jewelery, art, etc. It's like, "Here's a bunch of junk we collected when we were colonizing the world!" Anyway, The V&A has a large collection of locks and keys from throughout the ages. The day I was there, there was a large music and architecture festival going on called Explore Sights and Sounds. There was BBC-sponsored children's group performing a composition of their own making called "Encryption", inspired by the lock and key exhibit.