  In this article, we construct two continuous 1-parameter family of
non-compact $\mathrm{Spin}(7)$ metrics with both chiralities, with the
principal orbit an Aloff--Wallach space $N_{k,l}$ and the singular orbit
$\mathbb{CP}^2$. For generic $N_{k,l}$, metrics constructed are locally
asymptotically conical (ALC). For $N_{1,1}$, we construct two continuous
1-parameter families with geometric transition from asymptotically conical (AC)
metrics to ALC metrics.
