I'm going to run with this idea for a moment.
Lets call it Block Chain Link Fencing.
The ways to implement might include things like
1) merge mining the new chain
2) Finding the the unspent transactions
3) providing a way to move unspent transactions from the old chain to the new chain
(3) boils down to a checkpoint mechanism -- anything that can be done with two independent blockchains can be done inside a single one, if you can checkpoint the state in a way that's smaller than the full history of the blockchain. If you can't checkpoint them, you can't move them to another blockchain.
As a thought experiment, it's worth asking what the difference is between two blockchains and a single blockchain with a "version" counter that's incremented periodically (or a version bit, in the simplest case, so you can swap between the two). The answer is -- really, they're the same.