This sounds like a good case for a threshold signature scheme[1] where no one member has all of a complete key and can partially sign without revealing their piece of the key to anyone.
Aren't all algorithms "clever" at some level? I assume you are implying non-mainstream - that always carries risks, but there are some advantages:
1. The software that verifies the certificate doesn't need to be changed - which is quite an advantage if it has already been shipped, or if you need to change the signing rules at a later date.
2. The verification logic is exactly the same as if checking a regular, single signature certificate. Nice and simple, no bugs related to whether all criteria have been met by multiple certificates.