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There's lots of ways you might want to do this - in Pulumi, we often see folks using separate stacks for each of these environments, instead of using something like "stages" in APIGateway which are much more limited to only work with APIGateway (whereas you might want separate instances of other parts of your stack as well - like a separate DynamoDB Table, or a separate SNS topic, etc.). It's very easy to extend my gist from the parallel thread to stand up multiple stacks of that same program, each hosted at a separate subdomain:

<http://api-staging.lukestestapp.net|api-staging.lukestestapp.net>

,

<http://api.lukestestapp.net|api.lukestestapp.net>

(just make the subdomain a config variable and set it to different values in each stack).

Thank you @white-balloon-205! I'm also looking at this as a staging example: https://github.com/pulumi/get.pulumi.com/tree/master/infrastructure