Content instead of a block

I am not really familiar with Drupal yet, so I am not sure if I can describe my idea well enough but, who dares win, so I will give it a try!

I was thinking that when a site has lots of blocks on both sidebars, the Conversation Pivots block isn't the best way to show relative stuff. Is it possible that the block moves from one of the siderbars to right under the article/story/etc?