Q. How does Chicago style handle capitalization of add-on questions such as the following? “May I have a cookie? two cookies? four cookies?” Should the latter two questions start with a lowercase letter?

A. CMOS doesn’t cover this issue per se, but it incidentally shows an example at 5.229: “Which is better? And why?” In that case CMOS chose capital letters, perhaps because the add-on question can be seen as beginning a new sentence. You could view “Two cookies?” as an elision of “May I have two cookies?” and therefore as the beginning of a new sentence, or you could choose to view your add-ons as sentence-ending fragments, so that lowercasing is justifiable.