N users must approve a request I have a locked-down production system that we'd like to process specific requests, picked-up (poll) from a less-secure location.  For security and "go slow, this is production" reasons, a request must be authorized by 2 (or N) people on the team.

I can imagine how to implement this fairly simply just using openssl and signatures -- e.g., the secure server has a pool of public keys (people on the team who can authorize a request) and any submitted request must be correctly signed (e.g., https://stackoverflow.com/questions/10782826/digital-signature-for-a-file-using-openssl) with the private keys of N different people from that pool.

But it seems like a common-enough requirement that it must already exist; any pointers?  I have a suspicion I'm just not searching for the right terminology...  Thanks!
What you are describing is called $(t,n)$-threshold signature, where you need at least $t$ parties (out of a total of $n$) to create a signature. Considering your description, it seems that in your case $t=n$, so it is necessary that all the keys are used for creating the signature. 

This answer assumes that you want to verify the signature with a single public key (i.e., $n$ signatures, 1 verification). If you want to use $n$ public keys, then you can just require $n$ independent signatures.