  In this paper, we consider the modified two-component Camassa-Holm System
with multiplicative noise. For these SPDEs, we first establish the local
existence and pathwise uniqueness of the pathwise solutions in Sobolev spaces
$H^{s}\times H^{s}, s>\frac{3}{2}$. Then we show that strong enough noise can
actually prevent blow-up with probability 1. Finally, we analyse the effects of
weak noise and present conditions on the initial data that lead to the global
existence and the blow-up in finite time of the solutions, and their associated
probabilities are also obtained.
