When your 2010 Office 365 account is converted to 2013, you end up with 2 public web sites. Officially, you can only assign a personal domain to one of the sites but in reality it's quite easy with an Enterprise account to use a different personal domain for each site. I specifically cover adding sub domains here, but the same process applies to domains with a few adjustments.
As noted, this only works with Enterprise accounts and would be different - if even possible at all - for a P account. For small business accounts the workaround would be to url forward one of the domains to the least important site.
"Look Ma, 2 web sites with 2 separate domains!"
To see what I mean click here: http://365.webbrewers.com/Pages/webbrewerstest2.aspx
For a 2013 site see: http://365new.webbrewers.com
Both sites are in the same 365 account, but use different sub domains.
Instructions – set up in Sharepoint
If the parent domain is already verified, a sub domain will automatically verify. To verify a new sub domain, in 365 go to: Admin»Domains»Add a domain.
Enter your full sub domain (eg 365.domain.com)
Get the TXT record
Enter it at your domain host in the dns zone record section
Wait a few minutes and then click "Verify"
NOTE: If you have 2 public sites, apparently you have to enter the prefix for the sub domain as the host for the 2nd site, not the normal @ symbol.
Once it's verified, add any users you need
Select "Sharepoint" as the domain intent.
Go to the Sharepoint admin center, select the desired site and choose the sub domain from the drop down. When I did that I got a strange "Deleted" note by the default site name, but nothing was deleted and the site still worked under either the sub domain or the original default domain. MSFT couldn't tell me what the "deleted" referred to!
Instructions – connect your domain
Next, you'll point the sub domain at your 365 public site by adding an A record at your domain host.
Open a cmd screen and type in "ping your365domain-web.sharepoint.com" (without the quote marks and use the default domain, normally domain-web.sharepoint.com for 2010 sites, domain-public.sharepoint.com for 2013 sites).
Copy or note the ip address - it will be something like 126.96.36.199.
Go back to your domain host's dns zone record application.
Add an A record and enter the sub part of the sub domain as the host and the ip address as the target. For a domain, use @ in the host field.:
HOST POINTS TO TTL
365 188.8.131.52 600 seconds (or 1 hr etc) For sub domains
@ 184.108.40.206 600 seconds (or 1 hr etc) For domains
Save the zone file and within 15 minutes or so, your site should start coming up under the sub domain.
Why does MSFT tell me to use a CNAME instead of an A Record?
MSFT's instructions tell you to use a CNAME entry with the host set at "www". A CNAME is like an alias, so requests for www.domain.com are going to be sent to the server hosting domain.com to look for a site called "www.domain.com". That works if you only want the site to be found with a www request, or if all your sites are on the same host. If you use an A record, the request will be sent to whatever server the ip address entered represents. In other words, your site will be found with or without the www and you can use your domain with a site hosted in one place, and sub domains with your O365 site or vice versa. In my case, webbrewers.com is a WordPress site hosted outside of 365, and the 2 sub domains point to the 2 365 public sites.
Personally, I think it's a better arrangement.