Here's a passage written in 3/4 time:
(The composer uses an ambiguous shorthand after the first measure, but assume that where he wrote dotted-half tremolos he intended for the passage to be played 3 beats per measure with bow changes as spelled out in the first measure.)
Now suppose that along the way the composer wants to change the emphasis to two beats per measure, like this:
If this were a 4/4 ("common time") passage, something like this could be indicated with a change to 2/2 ("cut time"). But is there a time signature for this case of going from 3 quarter notes to 2 dotted-quarters?
My first guess was that the second example could be indicated with a time signature of 2/3. But I can't find any examples of such a time signature, and would any musician would understand that – especially if it weren't demonstrated explicitly in the first measure?