Google API: Get another user's email address by email alias

We would like to receive from Google a different email address of the user based on the email alias.

Note that this is not for the same user who authorized the app with Google OAuth, but for another user in the organization (otherwise the Google People API would be handy).

We have seen that this is possible with the Admin API, but this API is only available to organizational administrators and we must support regular users.

Background

When requesting information about another user's calendar using the Google Calendar API - only the primary email address can be used, email aliases are not recognized. The problem is that users have used their email alias many times rather than their primary email address.

Is it possible and how?