  Stereodynamic control of resonant molecular collisions has emerged as a new
frontier in cold molecule research. Recent experimental studies have focused on
weakly interacting molecular systems such as HD collisions with H$_2$, D$_2$
and He. We report here the possibility of such control in strongly interacting
systems taking rotational relaxation in cold collisions of HCl and H$_2$. Using
explicit quantum scattering calculations in full six dimensions it is shown
that robust control of the collision dynamics is possible even when multiple
(overlapping) shape-resonances coexist in a narrow energy range, indicating
that cold stereochemistry offers great promise for many molecules beyond simple
systems. We demonstrate a striking case where two prominent peaks in
overlapping resonances are switched-off simultaneously by suitable alignment of
the HCl molecule.
