  We construct the quantum s-tuple subfactors for an AFD II_1 subfactor with
finite index and depth, for an arbitrary natural number s. This is a
generalization of the quantum multiple subfactors by J.Erlijman and H.Wenzl,
which generalizes the quantum double construction of a subfactor for the case
that the original subfactor gives rise to a braided tensor category. In this
paper we give a multiple construction for a subfactor with a weaker condition
than braidedness of the bimodule system.
