I think the problem is, that at the base class, you don't necessarily know how to handle things, that are encountered at the concrete class level, or don't want to put the logic for all implementations into your base class. That would defeat the purpose of your abstract class and the hierarchy.
If you have to handle specific behavior for the new method in an existing type, of course you will need to add a new implementation of the method for that type.
As I understand the Expression problem, the limitation of programming languages is that they force you to modify the previous existing types even if the new behavior is a generic method that works the same for all types, so it should be enough to define it once for all classes. A virtual method in the base class should be able to do that.
That only moves the problem to the base class. In this case there is no difference in effort modifying the base class to foresee all cases that could happen with the derived classes, compared to adapting all the derived classes. In fact, you might even be typing more, because you might need some more "if"s in that base class, because you don't know which specific implementation you are dealing with, for which you implement the behavior in the base class. You still have to deal with the same amount of cases. And it is still bad, when you need to extend something that a library does, that you are not maintaining.
This does not solve the issue at its core, I think.