Hi @Aleph0,
Welcome to the community 
Things have moved on since this was first posted. To deploy upgradeable contracts we use OpenZeppelin Upgrades Plugins (https://docs.openzeppelin.com/upgrades-plugins/1.x/). OpenZeppelin CLI is no longer being developed (see: Building for interoperability: why we’re focusing on Upgrades Plugins).
For a multisig you may want to look at Gnosis Safe rather than Gnosis Multisig.
The following tutorials show how to upgrade a contract controlled by a Gnosis Safe.
- OpenZeppelin Upgrades: Step by Step Tutorial for Truffle
- OpenZeppelin Upgrades: Step by Step Tutorial for Hardhat
As for the cost of upgrading, you are deploying a new implementation contract each time you upgrade, so the cost of this depends on the price of gas (which increases with network congestion) and the price of Ether. Which at the moment means that any contract deployment is not a low cost exercise.