This is a system which consists of 4 (or more) parallel chains. Coins can exist on one of the 4 chains. Each transaction output would indicate the destination chain and it can only be spent in that chain.
In effect, blocks for all 4 chains can add to the UTXO set any chains, but only one of the 4 chains can spend each UTXO entry.
Each header points to a header from the previous chain. This creates a helix.
====A====A====A====A====
'. '. '. '.
=====B====B====B====B===
'. '. '. '.
======C====C====C====C==
'. '. '. '.
=======D====D====D====D=
Block N in chain B points to block N in chain A. Similarly for C and D. Block N + 1 in chain A points to block N in chain D. This creates a helix of block headers.
The combined header chain loops between the 4 sub-chains.
... A <- B <- C <- D <- A <- B <- C <- D ...
This means that nodes can prepare blocks in advance. If a sub-chain A block is the newest block found, then all the miners would be working on a chain B block. This block can only spend sub-chain B UTXOs. The miner can have a type C block ready and waiting to be mined. None of the inputs into the sub-chain C block can possible be spent by whichever sub-chain B block is found, since they all have to be sub-chain C inputs.
Once a miner hits their sub-chain B block, they can broadcast the header. All other nodes can immediately switch to mining their "pre-built" C block. They still need to follow up with the actual block within a short period.
This means that the block rate can be safely increased, since the propagation time for new blocks is reduced greatly (only an 80 byte header). If blocks ran at 10 mins per chain (so 2.5 mins combined), then the time to confirmation stays the same.
This reduces variance until a transaction is verified.
It means that distributed p2p systems for building up blocks would have time to build (and verify) new blocks and have them waiting in advance. This means that p2p miners might be possible. This is a p2p system that creates the blocks themselves, as opposed to p2pool which is a p2p mining pools, but each node produces their own blocks.