This is a very simple concept that may allow no limit to transactions per second on a blockchain
By having many entry points, transactions are channeled down to less servers or nodes residing on the more centralized crossroads of the internet.
These run fragments or branches of the blockchain based on block address. Each basically ends up with its own pool of money and verification of it.
So there are three tiers besides the merchants or users who send payments.
Spread all around the internet are the ‘closest’ nodes (7000). They package transactions by time and resend them as groups. Node types may be combined, by the way.
The next tier of 700 nodes, splits and reorders this data by index of address. They each create 70 different address-based groups, every time interval.
They send this indexed data to the 70 branches of the chain, who are running on any number servers.
Another 4000 nodes of various locations can be download and dissemination nodes. They receive updates of the chain and relay the information, allowing others to focus on receiving and consensus.
If one branch becomes overwhelmed it can split into two, publishing new address indexes, and this can go on indefinitely. Most transactions will end up in two branches.
Some Numbers
A branch is contained on multiple servers who create blockchain consensus. A server may contain multiple branches based on capacity, and alternate between what it receives. Branches need not intercommunicate excessively, since each has its own jurististiction.
Lets say users send 80000 transactions per second. They send over a few different routes, to as many reception nodes, belonging of the 7000. This means 80000 * 3 / 7000 equaling less than 50 transatios per second. That is very manageable. A node sends duplicate transaction-groups to a few of the 700 indexing nodes for about 2-7 routes.
So each second, a 2nd-tier node receives about 20-70 data chunks per second, which it splits up by address index. It sends separate packages to the 70 branches over 2-3 routes for ~150 outbound transmissions.
Much of this duplication is unnecessary, but may ensure integrity especially if all transmissions are totally one-way, like junk mail, for Sybil-resistant speeds.
Each physical server may have ~7 branches * 2.5 destinations each * 700/70 sending nodes = 175 address-indexed packages per second. It still must do normal blockchain consensus work too.
Conclusion
It appears to me that a group of people or entities can accomplish more than a single one, and these ideas above are based on this concept.
See omegakoin for more ideas.