Using external user as site collection administrator

Hi,

Is there a way to make a user who isn't a member of my Office 365 tenant a site collection administrator in SharePoint Online? (Preferably a plain Microsoft account with an Outlook address.)

Basically I have a software that requires site collection administrator privilages to access data from SharePoint, and I (my company) don't want to waste making a new tenant user just for this software. (And for a number of other reasons an external user would be highly preferred.)