How to I change the sort on a base application I have extended?

I have an application that I have extended. I want to be able to change the sort on the base application.

Initially, I tried customizing the base app setting but it looks like you can’t change the Sort Profile Selection on a customized app setting.

Then I tried creating a new application setting, but it looks like I can’t create a new Sort Profile Selection, I would need to use one that already exists on the base application.

What other mechanisms do I have available change the sort on a base application that I have extended?