  We investigate the possibility of multiple use of a single copy of
three-qubit states for genuine tripartite Einstein-Podolsky-Rosen (EPR)
steering. A pure three-qubit state of either the Greenberger-Horne-Zeilinger
(GHZ)-type or W-type is shared between two fixed observers in two wings and a
sequence of multiple observers in the third wing who perform unsharp or
non-projective measurements. The choice of measurement settings for each of the
multiple observers in the third wing is independent and uncorrelated with the
measurement settings and outcomes of the previous observers. We investigate all
possible types of (2->1) and (1->2) genuine tripartite steering in the above
set-up. For each case, we obtain an upper limit on the number of observers on
the third wing who can demonstrate genuine EPR steering through violation of a
tripartite steering inequality. We show that the GHZ state allows for a higher
number of observers compared to that for W state. Additionally, (1->2) steering
is possible for a larger range of the sharpness parameter compared to that for
the (2->1) steering cases.
