We have 5 domains, so each person has first.lastname.com and a full suite of email addresses if they choose. An expensive bit of fun but if all 5 were moved to GoDaddy, would they all be accessible via O365, or would one then need 5 O365 accounts?
So you have one domain and then everyone has a subdomain?
Looking at O365 Home (one subscription with up to 6 users / office licenses), this is not going to work:
While I assume (but I never checked) that it's possible to use a subdomain as well,
In O365 Home, the owner of the subscription is admin, sharing the licenses with up to 5 other users.
He (alone) can set up one (!) domain that all other users can use to create one email-address per user.
So: same domain / subdomain for all.
******@family.com + ******@family.com +...
IF dubdomains work in general (as said, I never checked);
you could only achieve this by using a number of individual O365 Personal licenses.
So everybody gits his own O365 personal license and then sets up his individual subomain.
But of course that's way more expensive.
So all in all:
sorry, not really a reasonable way to get done what you want.