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This paper is devoted to the study of noise effects on blow-up solutions tostochastic nonlinear Schr\"odinger equations. It is a continuation of ourrecent 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 thenon-conservative focusing mass-(super)critical case, by adding a largemultiplicative Gaussian noise, with high probability one can prevent theblow-up on any given bounded time interval $[0,T]$, $0<T<\9$. Moreover, in thecase of spatially independent noise, the explosion even can be prevented withhigh probability on the whole time interval $[0,\9)$. The noise effectsobtained here are completely different from those in the conservative casestudied in \cite{BD03}.

Stochastic nonlinear Schr\"odinger equations: no blow-up in the non-conservative case