We need the basis of a private ethereum-based blockchain.
Effectively, we need to recreate a stock transfer form as a smart contract that checks the validity of a trade request involving 2 or more token holders, and completes it if all of the elements are valid.
Of course, we also need a mechanism to generate the token
The contract code needs to be modular enough to be altered or maintained later down the line.
As the chain is private, the execution cost of the contract is less of a concern than it's security and stability.