I kindly received the following details from one of our developers who explained you can modify the list data, filtering logic, and styling in the Activities screen. You also have an extensible area to change or add buttons above the list in case you want to change create additional "subtabs" for the activities.
The list/columns are defined in this file on the Content Manager:
[TRIDION CME INSTALLATION FOLDER]\web\WebUI\Editors\CME\Xml\ListDefinitions\WorkflowDefinition.xml
Buttons and list control
The files for the Activities view, where the buttons and list control are rendered and styled, can be found in:
[TRIDION CME INSTALLATION]\web\WebUI\Editors\CME\Views\WorkflowActivities
The command buttons above the list are each associated with a command (e.g.
ShowAssignedActivities.js) which loads the relevant list data and also defines the filtering logic (including strings shown as a tooltip).
You can find the commands in the following directory:
[TRIDION CME INSTALLATION FOLDER]\web\WebUI\Editors\CME\Commands\WorkflowActivitiesPage
The area above the list is an extensible area, which means you can programmatically add extra buttons above the list as well as modify or otherwise swap out the commands used for the existing buttons.
Note: as a community wiki answer, feel free to add additional information, examples, or clarification.