There are a number of search widgets in the appstore that provide alternatives to the standard search capability. The one that works as you describe can be found here: https://appstore.home.mendix.com/link/app/49364/Mendix/Grid-Search
Hope that helps,
I just tested it in 7.11 and it works in my app. Here is how I configured it.
Here it is on the page:
Here are the properties of the widget
Here is how the grid is configured to eliminate the default search button:
and here is a video of the search working: https://youtu.be/RlnuI0vCi-M
This is not possible by default, as it is for a listview for instance. You can however work around this restriction. You can create your own 'custom search' by placing a input field above the datagrid on a 'surrounding' object, style it like a searchfield, and use its input in a datasource microflow when you can use to retrieve objects for your datagrid. Alternatively, you can put a new attribute on your object called '_SearchHelper' or something, that is filled using a beforeCommit action in which you concat all your attributes that you want to search on. For instance, $object/name + $object/place + $object/country resulting for instance in "BruceWayneGothamNepal". Then on your datagrid, use this field as your only search field.