  In this article, we construct a global martingale solution to a general
nonlinear Schr\"{o}dinger equation with linear multiplicative noise in the
Stratonovich form. Our framework includes many examples of spatial domains like
$\mathbb{R}^d$, non-compact Riemannian manifolds, and unbounded domains in
$\mathbb{R}^d$ with different boundary conditions. The initial value belongs to
the energy space $H^1$ and we treat subcritical focusing and defocusing power
nonlinearities. The proof is based on an approximation technique which makes
use of spectral theoretic methods and an abstract
Littlewood-Paley-decomposition. In the limit procedure, we employ tightness of
the approximated solutions and Jakubowski's extension of the Skorohod Theorem
to nonmetric spaces.
