Why you can mix into mediant, while not into supertonic 

Despite in theory it is correct, the so-called supertonic (ii) isn't one you want to mix into.
Take C major for example:
Play it and then a D minor on top; it'll sound horrible.
They're too close to eachother.
However, the so-called mediant (iii) will sound ok:
C Major to E minor.
There's no consensus within the DJ community for this 'rule/supertonic', see this overview:
docs.google.co...
...It's not working according to Mixed In Key either:
"So if we can go from 8B to 9A, why can’t we go from 8B to 7A? The scales of 8B and 7A contain dissonant intervals, so the mix wouldn’t work harmonically."
See: mixedinkey.com...
In general, the further away from eachother, the better they'll sound (within the chord).
See also: www.piano-keybo...
In reaction to 41:40 of • Pioneer DJ CDJ-3000 Re...