Banning users who change the user-agent

Is there a way to block users when the user-agent of their second request doesn’t match the user-agent of their first request?

I’m seeing this behavior with a lot of bad bots, probably in the hope that they will escape a ban placed on their user-agent. I’d like to be able to use this tactic against them, as no legitimate user is going to be changing their user-agent from one request to the next.