boost::static_visitor with multiple arguments

typedef boost::variant<int, double> Type;
class Append: public boost::static_visitor<>
{
public:
    void operator()(int)
    {}

    void operator()(double)
    {}

};

Type type(1.2);
Visitor visitor;
boost::apply_visitor(visitor, type);

Is it possible to change the visitor such that it receives extra data as follows:

class Append: public boost::static_visitor<>
{
public:
    void operator()(int, const std::string&)
    {}

    void operator()(double, const std::string&)
    {}
};

This string value changes during the lifetime of the Append object. Passing the string in via the constructor is not an option in this case.