CNAME for top of domain?
Solution 1:
Not possible - this would conflict with the SOA- and NS-records at the domain root.
From RFC1912 section 2.4: "A CNAME record is not allowed to coexist with any other data."
Solution 2:
You can setup your domain to be a CNAME to another domain, but then everything will go to that other domain -- including mail and the SOA "start-of-authority" record itself. However, you can still have separate subdomains, like "private.domain.com" use another mail and web server.