C#: Custom IEnumerator?

This is a message pertaining to C# in Unity, but I'm assuming general C# knowledge will apply.

Take the following code:

class myClass
{
    IEnumerator myEnumerator;
    public IEnumerator theEnumerator()
    {
        int i = 0;
        while (true)
        {
            Debug.Log(i++);
            yield return null;
        }
    }

    public void Update()
    {
        if (myEnumerator == null) { myEnumerator = theEnumerator(); }
        myEnumerator.MoveNext();
    }
}

If I instance that class, then call "Update" once per frame, I get the following output in the log:

0
1
2
3
4...

That works fine, however I want to implement some custom functionality in the IEnumerator itself. But if I create the following:

public class myIEnumerator : IEnumerator
{
    public int myCustValue;
    public void myCustFunction(){}
}

and then update the oringal class, replacing "IEnumerator" the "myIEnumerator", I get the following error:

The body of `myClass.theEnumerator()' cannot be an iterator block because `myIEnumerator ' is not an iterator interface type

What am I doing wrong here, and how can I make my own custom IEnumerator?