You could use LinQ to retrieve all files with multiple extensions like this:-
var files = Directory.GetFiles(@"C:\yourPath", "*.*", SearchOption.AllDirectories).
Where(s => s.EndsWith(".txt", StringComparison.OrdinalIgnoreCase) || s.EndsWith(".doc", StringComparison.OrdinalIgnoreCase));
Just be aware that the original query will return all files in yourPath, so if you pass in say C:\ you will start getting performance issues.