Yes, it is possible – see the anyone-can-* and target-adjust-freq blockchain parameters and the production notes at the bottom of the page:
https://www.multichain.com/developers/blockchain-parameters/
Please also consider the fact that, unless you make modifications to the MultiChain source code, it will use the same mining algorithm as the bitcoin network. This means your network will not be secure if some bitcoin mining power is used to attack it.
