  We generalise a recent example by F. Bracci, J. Raissy and B. Stens{\o}nes to
construct automorphisms of $\mathbb{C}^{d}$ admitting an arbitrary finite
number of non-recurrent Fatou components, each biholomorphic to
$\mathbb{C}\times(\mathbb{C}^{*})^{d-1}$ and all attracting to a common
boundary fixed point. These automorphisms can be chosen such that each Fatou
component is invariant or such that the components are grouped into periodic
cycles of any common period. We further show that no orbit in these attracting
Fatou components can converge tangent to a complex submanifold, and that every
stable orbit near the fixed point is contained either in these attracting
components or in one of $d$ invariant hypersurfaces tangent to each coordinate
hyperplane on which the automorphism acts as an irrational rotation.
