  This paper is devoted to the study of noise effects on blow-up solutions to
stochastic nonlinear Schr\"odinger equations. It is a continuation of our
recent work \cite{BRZ14}, where the (local) well-posedness is established in
$H^1$, also in the non-conservative critical case. Here we prove that in the
non-conservative focusing mass-(super)critical case, by adding a large
multiplicative Gaussian noise, with high probability one can prevent the
blow-up on any given bounded time interval $[0,T]$, $0<T<\9$. Moreover, in the
case of spatially independent noise, the explosion even can be prevented with
high probability on the whole time interval $[0,\9)$. The noise effects
obtained here are completely different from those in the conservative case
studied in \cite{BD03}.
