If you’ve set up distribution groups on Office 365, you will notice a section in the DG ‘details’ page titled ‘E-Mail Options’… under this title is the following text:
“The group can receive messages sent to the following addresses.”
From this, you can safely assume that it is possible to add e-mail aliases to the group so that the group can receive e-mails sent to several different e-mails.
Sadly, there is no easy way of actually doing this via the UI so it must be done via a PowerShell command…