Assuming you mean in-text citations. You do have abit more flexibility in footnote output syles.
So short answer, not very easily and it isn’t a very common practice, so unlikely that the developers will add as an option, but you can requestion it in the suggestions forum. The only “subsequent” citations setting available is the changes in numbers of Authors listed. Most of us rarely use that level of detail anyway, in a citation.
You will need to edit manually, with edit citation and add the suffix field. You could try to see if you could repurpose the Author (Year) option. Remember that none of these will automatically adjust if you introduce or delete a citation that was “first”.
Footnote templates do have a 1st and short form citation option, if you are using a footnote style. You would probably need to have the two forms of the journal in the record fields (Journal and Alternate Journal).