How to deploy a new proxy after ownership of the proxy admin has already been transferred to a multisig?

I have already deployed a number of proxy contracts using the upgrades package, and after doing so transferred the ownership of the proxy admin to a multisig.

Now, some time later, I want to deploy a new proxy contract (not upgrade an existing one) but I can not see a way to do so.

Calling deployProxy would require the multisig to sign, which is not feasible.

The function deployImplementation looked promising, however I could not see a way to provide intiializer arguments, which is necessary for this particular contract.

prepareUpgrade looks close to what I need, but it appears that this is only effective for contracts that the proxy admin is already in control of.

In essense, what I am looking for is the (new) deployment equivalent to prepareUpgrade, which does not appear to exist. Is there a way to achieve this?

Help would be greatly appreciated, thank you

Edit: Using openzeppelin/hardhat-upgrades@1.22.1

Is your intention to deploy an additional proxy contract that is still administered by the same proxy admin (which is now owned by the multisig)?

If so, you should be able to just deploy the new proxy using deployProxy -- the admin address is just a constructor parameter for TransparentUpgradeableProxy. I don't see a need for the multisig to sign at proxy deploy time.

(Note that deployImplementation and prepareUpgrade are both for deploying new implementation contracts, not for deploying proxy contracts, so those do not seem to be suitable for this scenario.)