just go to the object field definition page and in the fields and relationship just edit the Feed Item type Picklist and you can add you new vaalue in the picklist and save it again
I hope above solution will be helpful.
Go to Case page layout : You will find feed View click on that after that you will find all options
for more details you can visit this link:
Use Feed Filters to Manage Your Feed https://trailhead.salesforce.com/en/content/learn/modules/service_casefeed_basics/service_casefeed_basics_filters
I hope above information will be helpful.