  We discuss an extension of the scalar auxiliary variable approach, which was
originally introduced by Shen et al. ([Shen, Xu, Yang, J. Comput. Phys., 2018])
for the discretization of deterministic gradient flows. By introducing an
additional scalar auxiliary variable, this approach allows to derive a linear
scheme, while still maintaining unconditional stability. Our extension augments
the approximation of the evolution of this scalar auxiliary variable with
higher order terms, which enables its application to stochastic partial
differential equations. Using the stochastic Allen--Cahn equation as a
prototype for nonlinear stochastic partial differential equations with
multiplicative noise, we propose an unconditionally energy stable, linear,
fully discrete finite element scheme based on our augmented scalar auxiliary
variable method. Recovering a discrete version of the energy estimate and
establishing Nikolskii estimates with respect to time, we are able to prove
convergence of discrete solutions towards pathwise unique martingale solutions
by applying Jakubowski's generalization of Skorokhod's theorem. A
generalization of the Gy\"ongy--Krylov characterization of convergence in
probability to quasi-Polish spaces finally provides convergence of fully
discrete solutions towards strong solutions of the stochastic Allen--Cahn
equation. Finally, we present numerical simulations underlining the
practicality of the scheme and the importance of the introduced augmentation
terms.
