submitMulti does not change the authorization rules in Daml at all. Within a choice you still only have authorization of the signatories of the contract and the controllers of the choice. This is crucial to allow local reasoning about authorization. So a minimal example of something similar to your example is the following:
module Main where
import Daml.Script
template T
with
p : Party
q : Party
where
signatory p
nonconsuming choice CreateT : ContractId T
controller p
do create T with p = q, q
test = do
p <- allocateParty "p"
q <- allocateParty "q"
cid <- submit p $ createCmd (T p q)
-- fails due to missing authorization from q
submitMulti [p, q] [] $ exerciseCmd cid CreateT
What submitMulti allows (and the exact same thing applies to using multiple actAs parties on the ledger API) is to have more than one authorizer for the root commands of your transaction. So you could do a bare create that requires signatures from p and q or call a choice that has both p and q as controllers.
But within the body of a choice you only have authorization of signatories & controllers and there is no way to change that.