[Question] Is there a way to set the API Gateway stage on AWS different from the 'stage name' in the config?

[dsmurrell]

I have 3 stages... dev, staging, and prod. But I would like each of the three API Gateway endpoints to have a single API Gateway stage name of 'api' so that my app is accessible at '/api' on all three instead of '/dev', '/staging', and '/prod'.

I know about custom domains but this doesn't work for me because I share the domain with my front end client through a Cloudfront Distribution.

Is there a technical reason that there isn't configuration (that I can see) for this?