  Following the construction from `Degrees of growth of finitely generated
groups and the theory of invariant means' we generalize the Grigorchuk's
overgroup $\tilde{\mathcal{G}}$, studied in `On parabolic subgroups and Hecke
algebras of some fractal groups' to the family $\{ \tilde{G}_\omega, \omega \in
\Omega = \{ 0, 1, 2 \}^\mathbb{N} \}$ of generalized Grigorchuk's overgroups.
We consider these groups as 8-generated and describe the closure of this family
in the space $\mathcal{M}_8$ of marked groups.
