Shared Gateway, shared authorizer... 1 authorizer per stage?

I am in the early stages of architecting our microservices approach with Serverless. I have landed on taking the Shared Gateway / Shared Authorizer approach. We then break our domain up into seperate services (1 serverless.yml per service).

I have the Shared gateway spun up, and an authorizer wired in, but now I’m realizing that with this setup, I end up with that authorizer being shared by all stages.

My question is, do I want to end up with an authorizer per stage? Is that even possible?