Say the blockchain is split into 8 parts. Then the first 4 bits of an address would define which part of the blockchain it belongs to. Or the 5 first bits for 16 parts and so on. Every miner would than mine on only one of the parts of the blockchain. If a transaction has its sender and receiver in the same part of the blockchain, then the miners of that part will carry it out as usual. If sender and receiver are in different parts of the blockchain the miners of the senders blockchain check that the transaction is valid in the sense that the ether/gas is available and add it to the block as outbound transaction. After the block is confirmed say 16 times it will be processed by the miners of the receivers blockchain. That is to say the miners must look into the blocks of the other parts that are exactly 16 counts behind and processes all the outbound transactions that target the part of the blockchain that he mines on. If one of the other parts of the blockchain is not yet confirmed 16 times it has to wait until it is. 16 is of course just an arbitrary choice of mine.
Through consensus both parameters, the number of required confirmations as well as the number of parts of the blockchain could be changed at any point in time.
If you build a more sophisticated business logic with multiple contracts you could brute force them into the same part of the blockchain, so you don't have to wait 16 blocks when transactions go back and forth.
Such a split blockchain would be much more scalable as not all miners have to store and calculate everything that goes on in the network.
What do you think? Someone had this idea already?