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Cousin Jim.
It's what many do, since a bitcoind maintainer pumped p2sh multisig interest in early 2014. A lot of the services that built their product upon multisig today sprang from that wave (or the second one following all the fuckups, oof)
Fwiw, this works especially well across what you designate as security zones; I've had a wallet like that 2015-2018 until I rolled it over. It's still a pain to keep it secure though and no harder to secure your own 5 shares than 2 of your own and 3 or more of others! So you still need to solve the same problem in the end, but the defunct risk per-key is distributed and that is one worry less.
what you designate as security zones
Actually I do believe that was one of Bitmex's considerations, executives in different countries
It's still a pain to keep it secure though
Just ruminating on the scope the pieces add up, would need to be a working group thing
First there needs to be a coordination servers all parties use as a mailbox, a protocol for that... group invite flows...
Then you want different clients built with different stacks for different device hardware... basically a native android, native ios, native x64 for various OS's, native ARM for the same OS's... each leveraging hardware at the lowest possible level
Then you still need out-of-band coordination to prove a signing request is actually coming from the person its allegedly coming from, or to get hold of your co-signees
Need hooks into each of the signing apps to tie in any external polices people want
Probably need 4-5 people that know this shit very well to make something usable and it'll take months just to get it to a point where you start beating on it a bit
That sounds better than someone trying to manage 3 keys themselves across disparate devices and having to back up each, esp where I assume you'd have descriptors with each of your people as well
This is one direction my brain wanders into solving this issue, there's already a few paid services for this collaborative custody model and it replicates how enterprises deal with similar challenges. I even remember reading a Bitmex post from a hundred years ago about their withdrawal system needing multiple executives to approve.
Collaborative Cold Storage.
https://m.stacker.news/150385
This opens the design space quite a bit too. Imagine we humble stackers holding keys for one another.
There's other issues to mitigate, but it's worth exploring deeper how to standardize this.