Is it possible to set up a 2 out of 3 multisig AND a separate '1 out of all'?

[PrivacyG]

As I was reading about some multisig setups, this curiosity came to my mind.

Say I have three secure, privately owned locations.  My house, my farm and my apartment.  I can now set up a 2 out of 3 multisig.

But say I also have a fourth, extra secure location, such as a bunker no one can find or enter, hidden deep in the Ocean.  In my bunker, knowing no one will ever access it, I could store an emergency backup for my Bitcoin that would not require going to two separate locations to grab the Keys.

I do know the most basic answer would be having two or even all three Keys in the bunker.  But I have this curiosity, is it possible at all to set up a fourth Key that acts as an 'universal' one?

[Antidote47k]

Technically it should be possible. Bitcoin scripting allows alternative spending conditions, you can construct and analyze bitcoin spending policies with Miniscrpt. You would end up with four keys, A, B, C and D. The first three being the multisig setup and Key D being the master override.
The policy would be something like:
- Either two keys of A, B and C must sign or
- Key D alone can authorize.

Code:

 
 (A ∧ B) ∨ (A ∧ C) ∨ (B ∧ C) ∨ D

In simpler terms (2-of-3 multisig) or (Key D).

I think Taproot also offers another alternative, a single key spending path alongside a script path that enforces multisig.
Personally, I feel the setup defeats the whole aim of a multisig, which is needing more than a single key to authorize spending. If Key D were ever to be compromised then the multisig protection becomes null and void!

[Karl_3000]

I do know the most basic answer would be having two or even all three Keys in the bunker.  But I have this curiosity, is it possible at all to set up a fourth Key that acts as an 'universal' one?

These backup are all universal:

Seed phrase A, Seed phrase B, Master public key C
Seed phrase A, Seed phrase C, Master public key B
Seed phrase B, Seed phrase C, Master public key A

You can use any of the three as the fourth backup which can be used to get access to your bitcoin on the 2 of 3 multisig wallet.

Having two seed phrases of the multisig wallet and the third would be the master public key of there third seed phrase.

This is where I saw it: https://bitcointalk.org/index.php?topic=5595963.msg67210236#msg67210236

[Zaguru12]

I do know the most basic answer would be having two or even all three Keys in the bunker.  But I have this curiosity, is it possible at all to set up a fourth Key that acts as an 'universal' one?

I am confident that this is a possible where one key actually overrides the other co signers, I have read about Decaying multi sig before where over time one of the keys can be able to sign transactions alone, while this is different from your setup I think you can look into mini scripts too where you write a custom scripts about spending the wallet like you want, i don’t know if Sparrow wallet has actually started to support miniscripts descriptors[1].

Or better still uses something like a weighted multisig of 2-of-4 multi sig where the fourth seed phrase has two keys that can simply be able to sign the transaction although different from what electrum multi sig wallet with trustedcoin as co signer offers but it’s same.

My trade off though is that there is a single point of failure which is the fourth seed phrase and any one holding getting access to it can easily override the other co signed and technically this isn’t a genuine Multi sig wallet to be me.

Plus you would need to proper back up the public keys and the exact redeem scripts to generate the right addresses because the fourth key alone cannot do that for you.

[1]. Add support for miniscript descriptors

These backup are all universal:

This not what the OP intends, this is indeed a standard back up for 2-of-3 multi sig but OP wants to use a fourth key to be able act as a single sig and sign the transaction without needing the other co signers and not lookin for a universal back up actually

[nc50lc]

But say I also have a fourth, extra secure location, such as a bunker no one can find or enter, hidden deep in the Ocean.  In my bunker, knowing no one will ever access it, I could store an emergency backup for my Bitcoin that would not require going to two separate locations to grab the Keys.

Isn't storing two seeds and one extended public key in that bunker enough for that use-case?
Examples in Karl's reply.

While it's possible with OP_IF, OP_ELSE and OP_ENDIF scripts with CHECKMULTISIG and CHECKSIG as the two options.
Adding a single-sig option would defeat the purpose of the whole setup.