C++ override function and declare new with same name

I would like to extend a base class with a virtual function and keep the function name as virtual, but running code before and after the "possibly" overridden child function.

Here is an example:

I have a base class (interface) for things that can be drawn:

class IDraw {
    public:
        virtual void do_draw(Screen *scr) = 0;
};

I want to keep this interface in subclasses and be able to override it, for example I have a class for a Game, which cleans the screen, draw stuff and than flip the display buffer:

class Game : public IDraw {
    public:
        // Keep the interface
        // This can be overridden by sub classes
        virtual void do_draw(Screen *scr) = 0; // (1)
    private:
        // But override the base class so if s.b. calls
        // do_draw from a IDraw pointer it executes this!
        void IDraw::do_draw(Screen *scr) override; // (2)
};

// Implementation of (2)
void Game::IDraw::do_draw(Screen *scr) {
    // Do stuff before like clear the screen
    scr->clear();
    // Call the method supplied by childs
    this->do_draw(scr); // (1)
    // Present the drawing
    scr->present();
}

Since I have code before and after the function supplied by the child I cannot simply override keeping it virtual because the child must decide if calling Game::do_draw() // (2) before or after.

I know I can simply call the function (2) with a different name, but since I need many class doing this kind of stuff it will end with plenty of names for the same concept.

Is there any way to do this sort of thing in C++11?