  We analyse the STU sectors of the four-dimensional maximal gauged
supergravities with gauge groups ${\rm SO(8)}$, ${\rm
SO(6)}\ltimes\mathbb{R}^{12}$ and $[{\rm SO(6)}\times{\rm
SO(2)}]\ltimes\mathbb{R}^{12}$, and construct new domain-wall black-hole
solutions in $D=4$. The consistent Kaluza-Klein embedding of these theories is
obtained using the techniques of Exceptional Field Theory combined with the
4$d$ tensor hierarchies, and their respective uplifts into $D=11$ and type IIB
supergravities are connected through singular limits that relate the different
gaugings.
