I thought about that, and now I've had a follow-on thought and would like to know if what I'm about to describe is a speech quirk of mine, or if it's something that other people recognise as well.
Let's say that today is Wednesday the 1st, and I'm trying to make plans for Saturday the 11th.
I'll refer to Saturday the 4th as 'next Saturday' ("I'm not available next Saturday")
and Saturday the 11th will become 'Saturday next', ie: I'll leave the word 'after' out of the phrase 'Saturday after next' ("But we can meet up Saturday next")
I'd say that it was just a me thing - but no one's ever been confused when I've specified days like this.