Aggregating but not taking the first result
You can use the Views Field View module, like so:


Create a view "user profile" master (not page)


use contextual filter user UID
In the pager: Display a specified number of items : 1 item and set offset to 1

Create the main view


add global field view
use user uid as a contextual filter



The problem with this is that if user have only one profile then you may encounter a problem but maybe you can change it
for more detail on how to create view inside view check Drupal Views Inside Other Views.