The Cloud Computing Instances(CCI), have dedicated hardware CPU Cores. While the instance is virtualized for scalability and portability, the Hardware it runs on is Dedicated(not virtualized).

There are a couple of ways to get the upgrade you are wanting:

A) Request an OS reload via the portal and reloading to 2008 Enterprise edition, then afterwards order more cores for the machine.  This will require that you backup your data safely off of the server.

You did mention wanting to do this without a Reload, which I presume is for uptime of your sites. Unfortunately, the only way to achieve the upgrade of a single machine is through reload. As such, migrating to a new CCI may very well be more suitable to your liking.

B) Order a new CCI instance with Enterprise Edition and the number of core you would like then migrate the data over.