I remember thinking "I don't know if that's possible" but also thinking "does that question make sense"? If i use some xor/whatever to make 3 shards, don't I still have the original secret key. If that doesn't matter, and you just want the others to attest, or something, then just use their own keys? I guess I just don't get your point.

Obviously both N of N and M of N collaborative control of newly generated keys is well understood (albeit a bit complicated!).