Container of template classes without template parameter

I'm wondering if you can have a container with objects with varying template parameters.

I'm trying to achieve something like this:

#include <iostream>
#include <list>

template <class T>
class base
{
    public:
        T val;
        base(T newVal): val(newVal) {}; 
};

class derived : public base<int>
{
    public:
        derived(int newVal): base(newVal) {}; 
};

int main ( void )
{
    std::list < base<?> > base_collection;
    return 0;
}

I want my current project to be as flexible and dynamic as possible, with little extra coding when a new derived class is necessary, and my current implementation makes it important that such a list exists.

Is there a commonly used, benefiting and clean way of achieving exactly this?