I created an API Gateway using AWS CDK and I am using the serverless framework to create 3 different API's using the same API Gateway. My API Gateway structure looks like this:

/
  /service1
     /service1/{proxy}
  /service2
     /service2/{proxy}
  /service3
     /service3/{proxy}

I configured API Gateway as the origin of a cloudfront, redirecting requests coming from "domain/api" to API Gateway. The problem is that the path in API Gateway needs to match the selected path in cloudfront, so I would have to change it to something like:

/
  /api/service1
     /api/service1/{proxy}
  /api/service2
     /api/service2/{proxy}
  /api/service3
     /api/service3/{proxy}

This solution would be ok, but I can't share the "/api" path between multiple different services using the serverless framework. I would like the API Gateway rootPath to be "/api" and not "/", but I haven't been able to perform this configuration with the CDK. I wish I had something like this, is it possible?

/api
  /service1
     /service1/{proxy}
  /service2
     /service2/{proxy}
  /service3
     /service3/{proxy}

So that requests with /api were redirected by cloudfront to API Gateway, but could be defined as /service1 in the service, not /api/service1.