If you want to add a second website to your account, you would go and add an ADD-ON domain. You would still need to a registered domain name for the second website in order to get to it on the internet. Here's an article on how to utilize the ADD-ON domain option in the cPanel:
If you don't want to add the add-on domain name into your account, then you can always setup subdomain to the existing account and reference it using your IP address, or the subdomain reference. For example, if you have a primary domain named EXAMPLE.COM, then you can create a subfolder under it and then reference it as EXAMPLE.COM/newsite. If you don't want the folder searched as part of the current domain, then you can setup a robots.txt file in order to stop bots from crawling that subfolder.
I hope this helps to answer your question, please let us know if you require any further assistance.