sacredpath
(@sacredpath)
Automattic Happiness Engineer
Hmmm, that would be a pretty big project. You would have to create a child theme and then copy over the page templates that did not have a permanently visible widget area, and then register new widget areas in the functions.php file and then modify the html and CSS so that the new widget are would have room. This would be a very ambitious undertaking and require knowledge of php, html and CSS.
If you wanted to pursue this, I would suggest posting at https://jobs.wordpress.net and see what someone would charge you to make this sort of change.