  We formulate multiple Schramm-Loewner evolutions (SLEs) for coset
Wess-Zumino-Witten (WZW) models. The resultant SLEs may describe the critical
behavior of multiple interfaces for the 2D statistical mechanics models whose
critical properties are classified by coset WZW models. The SLEs are
essentially characterized by multiple Brownian motions on a Lie group manifold
as well as those on the real axis. The drift terms of the Brownian motions,
which come from interactions of interfaces, are explicitly determined by
imposing a martingale condition on correlation functions among boundary
condition changing operators. As a concrete example, we formulate multiple SLE
on the $Z(n)$ parafermion model and calculate the crossing probability which is
closely related to 3-SLE drift terms.
