  We prove the density property for generalized Calogero--Moser spaces with
inner degrees of freedom. This allows us to describe the holomorphic
automorphism group of these complex affine manifolds. These generalized
Calogero--Moser spaces can also be understood as quiver varieties corresponding
to moduli spaces of $\mathrm{SU}(2)$ instantons on a non-commutative
$\mathbb{R}^4$.
