  We continue our study for the stochastic defocusing mass crtical nonlinear
Schr\"odinger equation with conservative multiplicative noise, and show that it
is globally well-posed for arbitrary initial data in
$L_{\omega}^{\infty}L_{x}^{2}$. The main ingredients are several stability type
results for deterministic (modified) NLS, which have their own interest. We
also give some results on other stochastic NLS type models.
