Structure

interface IGameFrame
{
    void Update();
    void Render();

    void SetUp();
    void OnChangedToOtherFrame(newFrame);
    void OnKeyFirstDown(key, char);
    void OnKeyStillDown(key, duration);
    void OnKeyReleased(key);
    void OnMouseKeyFirstDown(key);
    void OnMouseKeyStillDown(key, duration);
    void OnMouseKeyReleased(key);
    void OnMouseWheel(delta);
}

class GameFrameMenu : IGameFrame
{
...
}

class GameFrameMain : IGameFrame { ... }

class GameFrameSettings ....
...

class Engine
{
...
    (public) IGameFrame currentFrame;
    (private) GameFrameMain frameMain;
    (private) GameFrameSettings frameSettings;
    (private) GameFrameXXX frameXXX;
    ...

    void Initialize()
    {
        frameMain = new GameFrameMain();
        ...

        currentFrame = frameMain;

        ...
    }

    void Update()
    {
        /*Handling input - then call currentFrame.On...*/
        ...
        currentFrame.Update();
        ...
    }

    void Render()
    {
        currentFrame.Render();
        ...
        //Overlays? Debug output ....
    }
    ...
}