Can you domain map www subdomain

I've been looking through the forums and there were quite a few topics but most were quite old.

I have one of my subsites wanting to domain map to the subdomain www level.

Can you do both an A record for top level AND a CName for the www?

They had a previous website using the www - when I domain mapped the top level domain with A record it goes to new site; however, if you add the www prefix it takes you to old site.

What needs to happen here?