Store derived class objects in base class variables

I would like to store instances of several classes in a vector. Since all classes inherit from the same base class this should be possible.

Imagine this program:

#include <iostream>
#include <vector>
using namespace std;

class Base
{
    public:
    virtual void identify ()
    {
        cout << "BASE" << endl;
    }
};

class Derived: public Base
{
    public:
    virtual void identify ()
    {
        cout << "DERIVED" << endl;
    }
};

int main ()
{
    Derived derived;
    
    vector<Base> vect;
    vect.push_back(derived);
    
    vect[0].identify();
    return 0;
}

I expected it to print "DERIVED", because the identify() method is virtual. Instead vect[0] seems to be a Base instance and it prints "BASE".

I guess I could write my own container (probably derived from vector) somehow that is capable of doing this (maybe holding only pointers...).

I just wanted to ask if there is a more C++'ish way to do this. AND I would like to be completely vector-compatible (just for convenience if other users should ever use my code).

What you are seeing is Object Slicing.
You are storing object of Derived class in an vector which is supposed to store objects of Base class, this leads to Object slicing and the derived class specific members of the object being stored get sliced off, thus the object stored in the vector just acts as object of Base class.

Solution:

You should store pointer to object of Base class in the vector:

vector<Base*> 

By storing a pointer to Base class there would be no slicing and you can achieve the desired polymorphic behavior as well.
Since you ask for a C++ish way of doing this, the right approach is to use a suitable Smart pointer instead of storing a raw pointer in the vector. That will ensure you do not have to manually manage the memory, RAII will do that for you automatically.