Will Falconer, DVM Moderator
I wouldn't, as parvo is the far greater risk, and we'd like the vital force of the pup to have a clear "message" at a time, not a mixed message.
Distemper is much more rare, though equally deadly. You'd hear about it if it was in your community.
Don's protocol is parvo once a week, so you'd likely have as good a result as mine with twice a week.