  We apply the dressing method on the Non Linear Sigma Model (NLSM), which
describes the propagation of strings on $\mathbb{R}\times \mathrm{S}^2$, for an
arbitrary seed. We obtain a formal solution of the corresponding auxiliary
system, which is expressed in terms of the solutions of the NLSM that have the
same Pohlmeyer counterpart as the seed. Accordingly, we show that the dressing
method can be applied without solving any differential equations. In this
context a superposition principle emerges: The dressed solution is expressed as
a non-linear superposition of the seed with solutions of the NLSM with the same
Pohlmeyer counterpart as the seed.
