[Valmont]

Although I think you mean something like this:

#include <iostream>
#include <string>
#include <vector>
#include <cstdlib>

using std::cout;
using std::cin;
using std::endl;
using std::string;
using std::vector;
using std::ostream;

//------------------------------------------------

class A
{
public:
  A(){}
  vector<string>& model_lookupTable()
  {
    return ModelLookupTable_;
  }
private:
  vector<string> ModelLookupTable_;
};

//------------------------------------------------

class Base
{
public:
  Base() {}
  Base( A& a ) : theA(a)
  {
     theA.model_lookupTable().push_back("Base") ;
  }
  virtual void some_function()=0;
  const vector<string>& get_table()
  {
    return theA.model_lookupTable();
  }
protected:
  A theA;
};

//------------------------------------------------

class Derived : public Base
{
  public:
    Derived(){}
    Derived(A& a) : Base(a) {}

    void some_function()
    {
      theA.model_lookupTable().push_back("Derived");
    }
};

//------------------------------------------------

int main()
{
  A myA;
  //Modfiy property directly.
  myA.model_lookupTable().push_back("A");
  //Constructor of class Base will modify property of class A.
  Base* myInstance = new Derived( myA );
  //Constructor of class Derived will finally modify property of class A.
  myInstance->some_function();

  //So what do we got for myInstance?
  for(unsigned i =  0; i < myInstance->get_table().size(); ++i)
  {
    cout<<"From instance: "<< myInstance->get_table()[i]<<endl;
  }
  
  //And class A?
  for(unsigned i =  0; i < myA.model_lookupTable().size(); ++i)
  {
    cout<<"Class A: "<< myA.model_lookupTable()[i]<<endl;
  }
  
  delete myInstance;
  return 0;
}