For example, I could use: myoldpasswordA1 / myoldpasswordB2 / myoldpasswordC3. Probably obvious to a human my next one will be D4, but it is a comparable problem to "play every possible game of chess" for a computer to figure that out.
Combined with using a secure computationally-expensive password storage mechanism (eg: bcrypt or PBKDF2) and I'm not exaggerating: it now takes billions of years to verify a password change is allowed.
And this is trying to solve a compromised password problem. If there's no compromise, rotating passwords is pointless.
If the password IS compromised, rotating the password doesn't really fix it, it merely limits access -- maybe. It doesn't address the original means of the compromise (so you have to assume that's still there). It doesn't address backdoors installed. It doesn't address information stolen.
So this is a hell of a lot of work to accomplish .. basically nothing.