Let $\Delta \subset \mathbf R ^2$ be an integral convex polygon. G. Mikhalkin introduced the notion of Harnack curves, a of real algebraic curves, defined by polynomials supported on $\Delta $ and contained in the corresponding toric surface. He proved their existence, via Viro's patchworking method, and that the topological type of their real parts is unique (and determined by $\Delta $). This paper is concerned with the description of the analogous statement in the case of a smoothing of a real plane branch $(C,0)$. We introduce the of multi-Harnack smoothings of $(C,0)$ by passing through a resolution of singularities of $(C,0)$ consisting of $g$ monomial maps (where $g$ is the number of characteristic pairs of the branch). A multi-Harnack smoothing is a $g$-parametrical deformation which arises as the result of a sequence, beginning at the last step of the resolution, consisting of a suitable Harnack smoothing (in terms of Mikhalkin's definition) followed by the corresponding monomial blow down. We prove then the unicity of the topological type of a multi-Harnack smoothing. In addition, the multi-Harnack smoothings can be seen as multi-semi-quasi-homogeneous in terms of the parameters. Using this property we analyze the asymptotic multi-scales of the ovals of a multi-Harnack smoothing. We prove that these scales characterize and are characterized by the equisingularity of the branch.