Return pointer to derived class from base class

I would like to now if the following is possible.

I have a templated class called A which inherits from a class called Base. In Base I set a write() function to be rewritten for every derived class.

I am creating a vector to store the references of the Base objects to be printer latter (dataBase).

I would like to know if it is possible to retrieve the reference of the A object whose reference I passed to dataBase.

I have the following code:

#include <iostream>
#include <string>
#include <array>
#include <vector>

class Base
{
    public:
        Base(std::string name):name_(name){}
        virtual ~Base(){}
        virtual void write()=0;

    const std::string& name() const
    {
        return name_;
    }
    
    private:
        std::string name_;
};

template< typename T>
class A : public Base
{
    public:
        A(std::string name):Base(name),name2_(name + "test"){}
        ~A(){}

        void write();

        std::string name2_;

};

template< typename T>
void A<T>::write()
{
    std::cout <<  name2_ << std::endl;
}


int main()
{
        
    A<int> one("one");
    A<double> two("two");
    A<std::array<double,4>> three("three");

    std::vector<Base*> dataBase;
    dataBase.push_back(&one);
    dataBase.push_back(&two);
    dataBase.push_back(&three);

    for(auto i : dataBase)
    {
        i->write();
    }

    A<int>& getOne = lookup("one"); // this is what I want to create
    getOne.name2_  = "worked";

    for(auto i : dataBase)
    {
        i->write();
    }

    return 0;
}

Best Regards