SSL Certificate for Internal Domain Controller

Hi, I need to install some SSL certificates on my 3 domain controllers to enable TLS.

I wish to use a third party CA (Symantec/Verisign) to produce the certificates. The domain my DC's are on is not public.

Is it possible to produce a certificate with our public facing domain name and use a Subject Name Alternative (SAN) option specifying the FQDN of the 3 domain controllers which can be installed on the domain controllers?

Or what is my solution here?

Thanks!