Template method pattern: changing the algorithm's architecture

I'm using template method pattern in my project like following

class Template
{
public:
void algorithm();
{
    A();
    B();
}
private:
virtual void A()=0;
virtual void B()=0;
}

I have some subclasses implement method A & B in different ways.
But now I need a new class Template2 to implement a slightly different algorithm.

class Template2
{
public:
void algorithm();
{
    A();
    B();
    C();
}
private:
virtual void A()=0;
virtual void B()=0;
void C()
{
    //some stuff
    A();
    //some stuff
    B();
}
}

C is identical along all subclasses, so I do not make it virtual.
Right now I create a new inheritance hierarchy based on Template2, but this seems stupid because I have to copy and paste every subclasses's code in this new hierarchy.
Is there anyway to do it in a more elegant way?