  We consider suspension flows over uniquely ergodic skew-translations on a
$d$-dimensional torus $\mathbb{T}^d$, for $d \geq 2$. We prove that there
exists a set $\mathscr{R}$ of smooth functions, which is dense in the space
$\mathscr{C}(\mathbb{T}^d)$ of continuous functions, such that every roof
function in $\mathscr{R}$ which is not cohomologous to a constant induces a
mixing suspension flow. We also construct a dense set of mixing examples which
is explicitly described in terms of their Fourier coefficients. In the language
of nilflows on nilmanifolds, our result implies that, for every uniquely
ergodic nilflow on a quasi-abelian filiform nilmanifold, there exists a dense
subspace of smooth time-changes in which mixing occurs if and only if the
time-change is not cohomologous to a constant. This generalizes a theorem by
Avila, Forni and Ulcigrai (J. Diff. Geom., 2011) for the classical Heisenberg
group.
