  In this paper we focus on the stochastic Euler-Poincar\'{e} equations with
pseudo-differential/multiplicative noise. We first establish two new
cancellation properties on pseudo-differential operators, which play a key role
in energy estimate. Then, we obtain results on local solution, blow-up
criterion and global existence. The interplay between stability on exiting
times and continuous dependence of solution on initial data are also studied
for the multiplicative noise case.
