A $k$-marked groups is a pair $(G,S)$ where $G$ is a group and $S$ is an ordered set of $k$ generators of $G$. Each such pair can be identified with a normal subgroup of the free group $F_k$ of rank $k$. Hence, the space of $k$-marked groups $\mathcal{M}_k$ can be identified with the set of normal subgroups of $F_k$ which has a natural topology (inherited from the set of all subsets of $F_k$) making it compact and totally disconnected.

My question is, can $\mathcal{M}_k$ be homeomorphic to $\mathcal{M}_\ell$ when $k\neq \ell$?