Setting up a secure2.mysite.com cert on a different server form secure1.mysite.com

Hello,
I have searched this forum and haven't found an answer to the exact question that I have so I apologize if this has been covered before, but I could not find it.

My question is this:
I have been running one server, we are in the process of migrating half those sites off to a new server as the server load is getting a little high.

I have a shared cert set up on server1 as secure1.mysite.com, I would like to setup a shared cert on server2 as secure2.mysite.com although the domain mysite.com will still reside on server1.

Before I go through the process of purchasing a cert, I'd like to know if this is possible. So what I'd like to do is install a cert for a domain that is not on the server. I do have the hostname set up as server2.mysite.com with a DNS entry on server1 that points to the IP of server2 and that works just fine. Or do I need to buy another domain for each server that I have to set a secure cert?

Thank you,
Andy