  In this paper, we present a pathwise construction of multi-soliton solutions
for focusing stochastic nonlinear Schr\"odinger equations with linear
multiplicative noise, in both the $L^2$-critical and subcritical cases. The
constructed multi-solitons behave asymptotically as a sum of $K$ solitary
waves, where $K$ is any given finite number. Moreover, the convergence rate of
the remainders can be of either exponential or polynomial type, which reflects
the effects of the noise in the system on the asymptotical behavior of the
solutions. The major difficulty in our construction of stochastic
multi-solitons is the absence of pseudo-conformal invariance. Unlike in the
deterministic case [47,54], the existence of stochastic multi-solitons cannot
be obtained from that of stochastic multi-bubble blow-up solutions in [54,57].
Our proof is mainly based on the rescaling approach in [39], relying on two
types of Doss-Sussman transforms, and on the modulation method in [16,44], in
which the crucial ingredient is the monotonicity of the Lyapunov type
functional constructed by Martel, Merle and Tsai [45]. In our stochastic case,
this functional depends on the Brownian paths in the noise.
