Overriding a method twice in a class

I need to override a method twice in a class for two different behaviors. example:

Abstract Class1:

public abstract class A : ReadVar_Class
{
public Ex_Interface ex_Interface1;

public abstract void AbtractExample();
}

I want to be able to define the abstract method for 2 different behaviors in another Abstract class. But i am not allowed to do it in the same class, is there a way i can achieve this? The constraint is that the framework is built with the abstract class type.

Abstract Class 2:

public abstract class B:A
{
 public override void AbstractExample()
  {
   ex_Interface1 = new InterfaceClass1();
   ex_Interface1.SearchField();
  }

public override void AbstractExample()
  {
   ex_Interface1 = new InterfaceClass2();
   ex_Interface1.SearchField();
  }
}

Thanks in Advance!