Triple flats and sharps and transposition

Suppose we have a passage that includes one or more notes spelled with a triple flat or triple sharp accidental mark (whyever that happens). Now we select the passage and apply a chromatic transposition up by an octave. Perhaps we should expect all the notes to retain their spellings but one octave higher on the staff.

(I say "perhaps" because my music theory background is so thin that I do not know what is prescribed by the accepted practice for this matter. So if the behavior I describe below is dictated, or suggested, by accepted music practice, never mind.)

But in fact all notes originally spelled with a triple flat or triple sharp mark are now enharmonically respelled, for a pitch one octave higher, in a spelling only using a single or double flat (or single or double sharp) mark.

Maybe this is odd. Maybe not.

Doug