EDIT: Can we just tweak the signature with the root MAST as well?
As I understand, the public key in scriptPubKey for P2TR is obtained by tweaking (let's call it original public key) and the root of the MAST. This original public key, in context of multi-signature,
is obtained by the process of Schnorr aggregation of the public keys owned by multiple participants. In the following, I will refer to the obtained public key (the one in scriptPubKey) as the P2TR public key.
What I'm interested in is how do we get a proper signature for such a P2TR public key?
If it was just one public key (not one obtained from multiple public keys), it would be easy. We would simply tweak the private key with the MAST root as well and then create the signature.
However, in the case of multisig (as far as I understand) the signature is created in such a way that all participants, each with their own private key, create partial signatures that are then merged into one. The problem is that this signature will match the original public key, not the P2TR public key that is in the scriptPubKey. So, the signature is not correct.
How is this overcome? How to make a correct signature in this case?