In theory, this is not possible. You can read about RFC2109 to get the technical specifications on what cookies can and cannot do.

The best you can do is set the cookie domain name as something like Domain=.mysite.com. This will allow www.mysite.com or abc.mysite.com to retrieve the cookie. Note that in both cases the domain name must be the same (which I assume that you do not want).

You can also use an IP address for a domain name. If different domains share the same IP address, you should be able to use the IP address as the domain on the cookie.

But then what happens if you need to move a site to a different IP address or change your IP address? Probably not a good solution.