  The pressure dependence of the magnetic and superconducting transitions, as
well as that of the superconducting upper critical field is reported for
CaK(Fe$_{1-x}$Ni$_{x}$)$_4$As$_4$, the first example of an Fe-based
superconductor with spin-vortex-crystal-type magnetic ordering. Resistance
measurements were performed on single crystals with two substitution levels
($x=0.033, 0.050$) under hydrostatic pressures up to 5.12 GPa and in magnetic
fields up to 9 T. Our results show that, for both compositions, magnetic
transition temperatures, $T_\textrm{N}$, are suppressed upon applying pressure,
the superconducting transition temperatures $T_\textrm{c}$ are suppressed by
pressure as well, except for $x=0.050$ in the pressure region where
$T_\textrm{N}$ and $T_\textrm{c}$ cross. Furthermore, the pressure associated
with the crossing of the $T_\textrm{N}$ and $T_\textrm{c}$ lines also coincides
with a minimum in the normalized slope of the superconducting upper critical
field, consistent with a likely Fermi-surface reconstruction associated with
the loss of magnetic ordering. Finally, at $p \sim$ 4 GPa, both Ni-substituted
CaK(Fe$_{1-x}$Ni$_{x}$)$_4$As$_4$ samples likely go through a
half-collapsed-tetragonal (hcT) phase transition, similar to the parent
compound CaKFe$_4$As$_4$.
