Wow! Thank you all for the quick responses. Using a utility class, as suggested by you and perrin, seems like an intuititive way of handling this problem in the general case, especially if the shared code were to use multiple objects.

After thinking more about the specific application, I realized that there is already "a good fit" for the utility method in ClassThree because all the shared work is just calling a handful of existing instance methods in ClassThree. The new method then becomes a shortcut instance method that calls a number of its own instance methods.