wordpress with multiple domains on shared host

I have a variety of sites sharing a single hosting account on crystaltech.
There is the main account domain, with several other sites being served based upon conditional code that looks at the domain name being requested.

They support wordpress.

I would like to use wordpress to create a couple of blogs, one each for a couple of sites. Is this possible?

For instance, I would like:
blog.domain1.com
blog.domain2.com