Alternative to the visitor pattern?

You might want to have a look at the Strategy pattern. This still gives you a separation of concerns while still being able to add new functionality without having to change each class in your hierarchy.

class AbstractShape
{
    IXmlWriter _xmlWriter = null;
    IShapeDrawer _shapeDrawer = null;

    public AbstractShape(IXmlWriter xmlWriter, 
                IShapeDrawer drawer)
    {
        _xmlWriter = xmlWriter;
        _shapeDrawer = drawer;
    }

    //...
    public void WriteToXml(IStream stream)
    {
        _xmlWriter.Write(this, stream);

    }

    public void Draw()
    {
        _drawer.Draw(this);
    }

    // any operation could easily be injected and executed 
    // on this object at run-time
    public void Execute(IGeneralStrategy generalOperation)
    {
        generalOperation.Execute(this);
    }
}

More information is in this related discussion:

Should an object write itself out to a file, or should another object act on it to perform I/O?

There is the "Visitor Pattern With Default", in which you do the visitor pattern as normal but then define an abstract class that implements your IShapeVisitor class by delegating everything to an abstract method with the signature visitDefault(IShape).

Then, when you define a visitor, extend this abstract class instead of implementing the interface directly. You can override the visit* methods you know about at that time, and provide for a sensible default. However, if there really isn't any way to figure out sensible default behavior ahead of time, you should just implement the interface directly.

When you add a new IShape subclass, then, you fix the abstract class to delegate to its visitDefault method, and every visitor that specified a default behavior gets that behavior for the new IShape.

A variation on this if your IShape classes fall naturally into a hierarchy is to make the abstract class delegate through several different methods; for example, an DefaultAnimalVisitor might do:

public abstract class DefaultAnimalVisitor implements IAnimalVisitor {
  // The concrete animal classes we have so far: Lion, Tiger, Bear, Snake
  public void visitLion(Lion l)   { visitFeline(l); }
  public void visitTiger(Tiger t) { visitFeline(t); }
  public void visitBear(Bear b)   { visitMammal(b); }
  public void visitSnake(Snake s) { visitDefault(s); }

  // Up the class hierarchy
  public void visitFeline(Feline f) { visitMammal(f); }
  public void visitMammal(Mammal m) { visitDefault(m); }

  public abstract void visitDefault(Animal a);
}

This lets you define visitors that specify their behavior at whatever level of specificity you wish.

Unfortunately, there is no way to avoid doing something to specify how visitors will behave with a new class - either you can set up a default ahead of time, or you can't. (See also the second panel of this cartoon )