How to install multiple Piggydbs on the same computer?

The Standalone Package doesn't support multiple databases. So you need to set up a Tomcat server (or other servlet containers) on your environment, to which you can deploy multiple War Packages. A database will be created for each deployment(installment) of the War Package.
Apache Tomcat -
To deploy a war file, just copy it to the webapps directory under the Tomcat home directory. You might want to change the name of the deployed war file corresponding to your purpose. The name will be used for the URL to access the application and the database file names (#16).