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.
Good thought experiment.
Storage size is one issue that link fencing would address with the additional linked chains. This could ultimately work with Bitcoin but for the very long term storage issues. There will be unspent transactions in perpetuity, but if each spend were made into the newer chains, only those old unspents would need to be tracked.
They are the same, but not really the same. We'd have to see it working in an alt for quite a while before monkeying with Bitcoin. The transaction volume issue is another place that could benefit from the BCLF model. Not entirely the same as one block chain, as it could also allow for feature additions in an incremental way.