We show that a perfectly genuine tripartite EPR steerable assemblage can be
distilled from partially genuine tripartite EPR steerable assemblages. In
particular, we consider two types of hybrid scenarios: one-sided
device-independent (1SDI) scenario (where one observer is untrusted, and other
two observers are trusted) and two-sided device-independent (2SDI) scenario
(where two observers are untrusted, and one observer is trusted). In both the
scenarios, we show distillation of perfectly genuine steerable assemblage of
three-qubit Greenberger-Horne-Zeilinger (GHZ) states or three-qubit W states
from many copies of initial partially genuine steerable assemblages of the
corresponding states. In each of these cases, we demonstrate that at least one
copy of a perfectly genuine steerable assemblage can be distilled with
certainty from infinitely many copies of initial assemblages. In case of
practical scenarios employing finite copies, we show that the efficiency of our
distillation protocols reaches near perfect levels using only a few number of
initial assemblages
