Using TFS API you connect to your test case and add a new column to it's datatable or you modify a currently existing column. But beware, all test cases use the same parameter set, if you add them via "add existing". Only if you do choose "copy and add to suite", then you have a new test case with its own parameters table.
You can use the TFS API either with C# and create an .exe file or you can also use PowerShell or even C# in PowerShell:
using (TfsTeamProjectCollection tp = new TfsTeamProjectCollection(collectionUrl))
{
var tm = tp.GetService<ITestManagementService>();
var tp = tm.GetTeamProject(teamProject);
var tc = tp.TestCases.Find(testCaseId);
tc.Data.Tables[0].Columns.Add("MyParam", typeof(String));
tc.Data.Tables[0].Rows[0]["MyParam"] = "WinnerWinnerChickenDinner";
tc.Save();
}