  In this paper, we study the Cauchy problem for the stochastically perturbed
high-dimensional modified Euler-Poincar\'{e} system (MEP2) on the torus
$\mathbb{T}^d$, $d\geq 1$. We first establish a local well-posedness framework
in the sense of Hadamard for the MEP2 driven by general nonlinear
multiplicative noises. Then two kinds of global existence and uniqueness
results are demonstrated: One indicates that the MEP2 perturbed by
nonlocal-type random noises with proper intensity admits a unique large global
strong solution; The other one infers that, if the initial data is sufficiently
small, then the MEP2 perturbed by linear multiplicative noise has a unique
global solution with high probability. In the case of one dimension, we find
that the stochastic MEP2 will break down in finite time when the initial data
meets appropriate shape condition.
