Can't figure out how to share some code

Question

I have some code which I want to pull out of a class so I can share it with other classes. I can't figure out how to do it with the restrictions that I have. Here is my situation.

I have a class B which inherits from a 3rd party base class A. The restriction is that I can only have one class in my project which inherits from base class A due to the way the larger system we are working on is design.

public B : A
{
   private void MakeLunch(int numLunches)
   {
     for (int i=0; i < numLunches; i++)
     {
       .... // get bread, ham, etc.
       .... // put mayo on bread, slice ham, etc.
       base.MakeSandwich(bread, ham, ...); // MakeSandwich()   is   protected
     }
   }
}

Originally, I tried taking out MakeLunch() into its own class (class C) and deriving from class A so I can get the MakeSandwich() method, but I found out that only one class in my project can derive from class A. (create class C in another project is not an option)

I then tried to pass a reference to class B when I create class C but the MakeSandwich() method from class A is protected.

Anyone know of a way for me to pull out my MakeLunch() method into its own class?