Extending GroupPrincipal and Members property

Question

I want to extend the GroupPrincipal class to handle some custom properties:

using System.DirectoryServices.AccountManagement;

[DirectoryRdnPrefix("CN")]
[DirectoryObjectClass("group")]
public class MyGroupPrincipal : GroupPrincipal {
    // ...
}

How could I override the Members property for MyGroupPrincipal so that if it has a member that is a group an instance of MyGroupPrincipal and not of GroupPrincipal is returned? I would like to write e.g.

MyGroupPrincipal group = GetGroup();
foreach (var m in group.Members) {
    if (m is MyGroupPrincipal) { // always fails: m is a normal GroupPrincipal 
        // do something
    }
}