Is there a way to share apps with multiple people so they can download the latest APK from their sandbox app market without having to change package names and uploading to each Developer member?
Currently, an app in development can only be accessed and downloaded by one account. To share this with others APKs need to be uploaded with a different package name on their dev environment account else it can't be uploaded and they can't have access to it.
I believe I understand your question a bit better.
For the sake of sharing apps within a development team (for multiple people working on the same app), you can take advantage of the members feature on your developer account.
You cannot download apps that are not your own in sandbox. If the app is not uploaded on your developer account, you cannot download it. This is intended, as Sandbox is strictly an environment for development.