We had exactly this scenario on a large project where the derived methods were called from various locations. Due to change management and QA scripts not to be broken, among other constraints, "drastic" refactoring and class re-structuring are not always possible on a large mature project. Also we did not want to override the method and exclude all base functionality. Most solutions seen elsewhere, looked a bit clumsy, but the solution from Josh Jordan on How to call base.base was quite useful. 
However we followed the approach below (which I see now is very similar to what Dan Abramov propose).
public class Base
{
    public virtual void Foo()
    {
        Console.WriteLine("Hello from Base");
    }
}
public class Derived : Base
{
    public override void Foo()
    {
        base.Foo();
        Console.WriteLine("Text 1");
        WriteText2Func();
        Console.WriteLine("Text 3");
    }
    protected virtual void WriteText2Func()
    {
        Console.WriteLine("Text 2");
    }
}
public class Special : Derived
{
    public override void WriteText2Func()
    {
        //WriteText2Func will write nothing when method Foo is called from class Special.
        //Also it can be modified to do something else.
    }
}