Can another section for adding a web part be added to a Blank Site using UI?

Hello Community

    Using Sharepoint 2010 Server and the UI you can create a "Blank Site".
  
    When you click Edit Page the Blank Site at the top there will be the word
"Left" and underneath that "Add a Web Part" and to the right the word
"Right" will be displayed and beneath that "Add a Web Part".

    The question is, is there a way to create a section that allows you
to add another web part?

    Thank you
    Shabeaut