They can make an altcoin and voila, they'll have a blockchain.
But there's no stronger blockchain than Bitcoin's. And if that's advertised enough, organizations will come for the blockchain and will have to use bitcoin for that.
For the moment, the bitcoin blockchain is the most 'used' and it is the most secure but like I said "for the moment". However it is normal that in the future someone will build something better than the actual bitcoin (this is obvious... technology).