How to group multiple blocks into one big block
Block Group module may help you


  This module extends the standard drupal block system with block
  groups. Each block group provides a new block as well as a
  corresponding region. Child blocks can be moved into any group region.
  The position and the settings of the parent block are propagated to
  its children. Also block groups are nestable.


Take a look. I am not sure how it will integrate with responsive style.