Polymorphic factory

Consider the following code:

template <typename T>
class DrawerFactory
{
protected:
    DrawerFactory() {};
private:
    virtual shared_ptr<IDrawer> GetDrawer(T settings) = 0;
};

class ConcreteDrawerFactoryA : public DrawerFactory<SettingsA>
{
public:
    shared_ptr<IDrawer> GetDrawer(SettingsA settingsA) override
    {
        if (settingsA.style == A) return make_shared<ConcreteDrawerA>(settingsA.length, settingsA.stroke, settingsA.opacity);
        else return make_shared<ConcreteDrawerB>(20, .5);
    };
};

class ConcreteDrawerFactoryB : public DrawerFactory<SettingsB>
{
public:
    shared_ptr<IDrawer> GetDrawer(SettingsB settingsB) override
    {
        if (settingsB.type == TYPEC) return make_shared<ConcreteDrawerC>(settingsB.width, settingsB.height);
        else return make_shared<ConcreteDrawerD>(10, 2);
    };
};

I can get a drawer by:

ConcreteDrawerFactoryA().GetDrawer(settingsa);

or

ConcreteDrawerFactoryB().GetDrawer(settingsb);

What I'd like to do is:

DrawerFactory().GetDrawer(settingsa);
DrawerFactory().GetDrawer(settingsb);

Is there a way to set this up without having to continually add overloads to DrawerFactory for each concrete factory I want to add?