  We consider a stochastic nonlinear Schr\"odinger equation with multiplicative
noise in an abstract framework that covers subcritical focusing and defocusing
stochastic NLS in $H^1$ on compact manifolds and bounded domains. We construct
a martingale solution using a modified Faedo-Galerkin-method based on the
Littlewood-Paley-decomposition. For 2d manifolds with bounded geometry, we use
Strichartz estimates to show pathwise uniqueness.
