  Recent studies of strong interaction effects in kaonic atoms suggest that
analysing so-called `lower' and `upper' levels in the same atom could separate
one-nucleon absorption from multinucleon processes. The present work examines
the feasibility of direct measurements of upper level widths in addition to
lower level widths in future experiments, using superconducting
microcalorimeter detectors. About ten elements are identified as possible
candidates for such experiments, all of medium-weight and heavy nuclei. New
experiments focused on achieving good accuracy for widths of such pairs of
levels could contribute significantly to our knowledge of the $K^-$-nucleon
interaction in the nuclear medium.
