You could split wood more than 2 ways, then register one of the pieces. Or a system of splitting multiple pieces of wood, leaving some for registration. No idea if this is what anyone has done.
But if you have a system where you can register the stick then why do you need the stick? Just register the contract with this, apparently trusted, 3rd party.
The third party and the registered stick slice aren't required to add marks to the outstanding sticks.
Splitting more tallies from one stick was done on certain occasions, especially if intentional fraud was a concern.