Q:

How to invoke the base and overloaded constructors at the same time?

I want to invoke the overloaded ctor via this and the base ctor via base as follows.
public Child(string msg, DateTime dt) : base(msg, dt), this(msg)
    => WriteLine($"Child at {dt.Second}");

Apparently it will not compile.
Question
How to invoke both? Is it impossible?
Note that I am not asking how to invoke the contents of the corresponding ctors by rearranging them.
using System;
using static System.Console;

class Parent
{
    public Parent(string msg)
        => WriteLine($"Parent {msg}");

    public Parent(string msg, DateTime dt) : this(msg)
        => WriteLine($"Parent at {dt.Second}");
}
class Child : Parent
{
    public Child(string msg) : base(msg)
        => WriteLine($"Child {msg}");

    public Child(string msg, DateTime dt) : base(msg, dt)//, this(msg)
        => WriteLine($"Child at {dt.Second}");
}
class Program
{
    static void Main()
        => new Child("hi", DateTime.Now);
}

A:

Yes, it is impossible. There is no such construct in C#. The reason is that a constructor always invokes the base's constructor; when there is no specific constructor denoted by base(…), the default constructor is invoked.
However, a simple private method will serve the same purpose:
class Child : Parent
{
    public Child(string msg) : base(msg)
        => ChildInit(msg);

    public Child(string msg, DateTime dt) : base(msg, dt)
    {
        ChildInit(msg);
        WriteLine($"Child at {dt.Second}");
    }

    private void ChildInit(string msg)
        => WriteLine($"Child {msg}");
}

