  We analyse the energy supercritical semilinear wave equation
$$\Phi_{tt}-\Delta\Phi-|\Phi|^{p-1}\Phi=0$$ in $\mathbb R^d$ space. We first
prove in a suitable regime of parameters the existence of a countable family of
self similar profiles which bifurcate from the soliton solution. We then prove
the non radial finite codimensional stability of these profiles by adapting the
functional setting of arXiv:1912.11005.
