I assume that you are talking about a token on the Ethereum blockchain and you would like to make some short of parallel transactions that are mineable instead of just having your token out there being transfered on the blockchain? For a transaction to occur you would need to mine it on the Ethereum blockchain and I think that you can reward the miner of that transaction with your token, but I am not sure if that is what you want.

It looks a bit complex, but it is most likely possible with smart contracts. Make sure you clearly define the "problem" to get a better answer.