I understand that "classic" bitcoin multisig transaction contains following parts: 1) Amount sent to another BTC address, 2) fee, 3) UTXO, which can be returned back to original source address or other address (in same HD wallet). I am wondering if the same transaction, that is being signed by multiple parties, can contain more of (1) - more destination addresses. In other words - is it possible that mediator, who has the role of escrow, can charge fee that is paid by the very same transaction that both seller and buyer sign? Thanks
To clarify, a transaction spends one or more inputs (which are outputs of previous transactions) and creates one or more outputs (often including a "change output" sending excess value back to the sender). The mining fee is only given implicitly by the difference between the total input and output values.
If a transaction contains one or more inputs whose prevouts are encumbered with a multisignature script, we might call it a multisig transaction, but the multisig only really happens at the individual input level. The signature accompanying this input must be a result of an agreement between multiple parties, but this doesn't place any other limitations on what the transaction can look like, as long as the parties agree on it. A multisig transaction can have a hundred outputs to a hundred different addresses, just like a non-multisig transaction.
So yes, it is definitely possible for the escrow to have an output that pays them a fee in the transaction that also pays out the seller.