I think that what you want to do is to start by creating a Browser Custom Field, you can do this from your Settings > Fields.
While doing this make sure to assign this field to your Test Sets (when you scroll down on the page where you create the field). https://www.practitest.com/help/settings/custom-fields/
Once you have this, you can create a test set and assign it to a specific browser, then you can clone it for each of your browsers or use the permutations function (you can read this here)
Alternatively, you can add the same test multiple times to the same test set and have multiple instances of this test, where each is assigned to a different browser. If you want to do this, then instead of assigning the custom field for the Browsers to the Test Set, then do it for the Instances.
You can also see this video that shows part of this process.