Continuum-many discontinuous actions of ${\mathrm{SL}}_{n+1}(\mathbb{Q})$ on manifolds

For any $n\ge 1$, we construct a continuum of non-conjugate actions by homeomorphisms of ${\mathrm{SL}}_{n+1}(\mathbb{Q})$ on the $n$-sphere $S^n$ that do not extend to a continuous action of ${\mathrm{SL}}_{n+1}(\mathbb{R})$. We do this by adapting a blow-up construction of Bowden and Mann. We motivate studying these actions and note down some related observations.