Unique Modules on Profile pages

Hi...

CB 1.8.1
J! 2.5.6

I have a site that is city based across North America. I have created filtered lists that offer profiles per city. When a user clicks on a profile from one of those lists, I loose the ability to place a module (preferably a blank Mod) on the left hand side. I need this as the profile needs to be shifted to the right by at least a mod width so that it is more readable and does not get effected by my background.

So basically how do I place a mod on a profile page?

Can anyone help with this?

I need modules on the PROFILE pages I may have thousands so cannot create unique links to the profiles, how do I get them assigned to that page?