Extending a general purpose function

I'm creating a game, and in this game a ball can be caught in various ways, which all result in different behaviour. Initially, I wanted to add an enum to a certain general purpose method when catching to ball, which will then delegate the actions that take place when a ball gets caught in a certain way. An example would be:

void Weapon::Catch(Character Catcher, CatchMethod Method)
{
    switch (Method)
    {
        case Method::PickUp: OnPickup(Catcher); break;
        case Method::Pass:   OnPass(Catcher);  break;
        // etc
    }
}

This would allow me to call the function as:

MyWeapon->Catch(Catcher, Method::Pickup);
MyWeapon->Catch(Catcher, Method::Pass);

and the likes. I think this would read nicer than

MyWeapon->CatchByPickup(Catcher);
MyWeapon->CatchByPass(Catcher);

My main issue however, is that this is not extendable at all, which is what I was actually hoping to achieve with this general purpose method. If I make the method an enum, I cannot simply extend the enum and override the virtual Catch method in a derived class of Weapon. If I decide to extend the method in some derived class, I'd have to create a new enum which begins at the last value of the Method enum. I do not feel that this is a proper way to deal with the situation, but I do not know what the best practise in this case would be. Does it perhaps involve template specializations?