Author-date style with more than 26 references per author per year?

I've been asked to use an author-date citation style, so I've looked at APA and Harvard. Both styles sort references chronologically, assigning the publication year followed by an alphabetic letter as a unique identifier. This works fine if there are 26 references per author per year or fewer, as there's a unique letter available for every reference within any given year. However, with 27 references or more, once the 'z' has been assigned, this system falls down and Zotero gets confused.

Is there a solution to this problem other than not using an author-date style in the first place?
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