Make it a 5-of-7 instead of a 4-of-6
If the four parties are the payer, payee, and two mediators, then the redeem script could be a p2pkh script for an address controlled by the payee OP_AND a 3-of-3 multisig with the payer and the two mediators.
Certainly, however the question specifically asked about:
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where the two parties are not the signatories required to release the funds and any four of the six escrow could sign to release
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So that should have been four mediators.
Still, the point is the two scripts connected with an OP_AND approach vs the "higher m and n" approach.
So, you are saying the exact same thing as I did?
The transaction will require a total of 5 out of 7 possible signatures.
It will require:
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that one of the 5 signatories be the recipient
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OP_AND
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the approval of at least 4 of the remaining 6 signatories.
1 required recipient sig + 4 required escrow sigs =
5 total sigs required (M)1 recipient sig possible + 6 escrow sigs possible =
7 total sigs possible (N)M-of-N is 5-of-7 with one of the 5 sigs being required to be from the recipient.