Customize "My Profile" Page

Not possible. The User Profile secition is one of the least customizable parts of Gainsight CC platform. 

Your options for customizing are limited to 

1. Profile fields
   1. Public fields are fully public, even visible to logged-out/unregistered users,
   2. Private fields are fully private, visible only to admins and the user themself
   3. There is no hybrid option where other users can see it, but logged-out users cannot. There should be an idea for it somewhere on here. 
2. Anything you can hide via custom CSS
3. If a user chooses to display their rank, etc via settings

there are not any other widgets you can pull in. You can submit these as ideas and I’d definitely vote for them. But in my 3+ years as a customer, I haven’t seen profiles as an area of investment or product enhancement (outside of updated notification settings).