Multi-Signature – Spending Path for a Subset of n-of-n Multi-Signatures

I would like to achieve the following:

group N People come together to create n-of-n multi-signatures. Each of them funds this multisig with custom Bitcoin. At some point in the future, they decide to use these funds. K One of the initial groups has disappeared or is no longer responding.

Is it possible to achieve the following behavior?

• that much K Those who do not respond will receive back the funds they originally donated.
• left (N-K) Those who can sign agree together on where the remaining funds will be sent. By default, multisignatures appear to be (NK)-(NK) from the beginning.

I was thinking that one possible approach (correct me if I’m wrong) would be to use some taproot functionality and include different spending paths in the Merkle tree that would allow all possible subsets of users to spend, as described above. This is achieved by pre-signing multiple transactions during multi-signature generation using these different spend paths. These transactions are signed in such a way that the output returned to the unresponsive user is predefined, and for the remaining funds, the remaining users must unanimously decide and agree on where to send them when the time comes. come.

Will this work? Even if the answer is yes, as the number of users increases, the combination of subsets will grow exponentially, making this impossible, so there may be a better way.

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