I’m a big fan of just putting it out there, on the theory that if they don’t like your thought process on something like this, that might be a sign that they won’t like it on other things too, and better to just be transparent and figure out if that works for them or not.
(I mean, don’t reschedule so quickly that you don’t have time to thoroughly prepare — but don’t stall just because it feels awkward.)
Hopefully you won’t get job offers on the exact same day or need to give notice on the exact same day, so whoever accepts an offer first will give notice first, making no mention of the other person.
I’ve been asked to give a reference for two people for the same job
I work in a fairly competitive, but still small, field, where getting a job is all about who you know.