Hello John,
Thank you for your question and your interest in W3 Total Cache Pro!
You should have no problem running Pro on your Dreamhost!
W3 Total Cache Pro licenses are valid on a per-install basis, meaning you need one for every WordPress instance you run. If you have three separate websites, you will need three licenses in total—one for each site. If you have five sites in a WordPress multisite instance, you need just one license for all five sites. If you are interested in bulk licensing, please email us for more information.
Thank you!