What is the intent here?
- “the country the requestor belongs to”
Security Requirement
Is that a security requirement?
- A Singaporean user is the only one allowed to search/see Singaporean cases?
If so, customizing search to achieve would be the wrong approach (access control / security should be applied to stop this kind of access)
Promoted Filter
Is this a UX requirement?
- “I want to show Singaporean cases to my Singaporean users as they are the cases they are most likely to want to see”.
If so, then there would be a need for the user to change from Singapore to All or maybe a specific country (E.g. Japan). In this case, Global Search would not be appropriate as you have no authoring ability to add new filters/fields to the landing page.
Constellation makes authoring landing pages, with your own Filters and Results really easy. I’d be looking at configuring this, than trying to customize. Some videos from our 
Webinar Replay: Achieving outcomes in Constellation: Solution Designing and Building for Success last week:
Other requirements?
Given you’ve started to look at configuring this page, like above, you’ll probably have needs to show different fields/columns, views, sorting/filtering, grouping etc. Using Insights or List Views would give you far more control over these.
Personally, I’m not a big fan of Global Search. I think we can create much richer experiences with landing pages/insights/dashboards - its a good starting point, gets you searching quick but once you start getting requirements like these, it is probably a good point to look at configuring your own experience.
Constellation 101
If you haven’t seen this before, it may help if you continue to go down the path of customizing Global Search.
Constellation Tips: Display custom property values in the full text search results (Global Search)