  Recently, it was shown that type D black holes, encompassed in the large
Pleban\'ski--Demia\'nski (PD) family, exhibit a wide class of algebraically
general generalizations via the application of Ehlers and Harrison
transformations. In this work, we first discuss some mathematical details
behind the composition of such transformations, and next, we introduce a
qualitative picture of the most general type I generalization of the PD family,
dubbed ``Enhanced Pleban\'ski--Demia\'nski'' spacetime. We provide the exact
form of the solution in the original PD coordinates, obtained via the
simultaneous action of an Ehlers and a Harrison transformation on the vacuum PD
geometry. In order to make the physics more transparent, we explicitly
construct a rotating and accelerating black hole which further has NUT
parameter and electric charges, both of them entering, not only the event
horizon, but the Rindler horizon as well. This solution is directly obtained in
the ``physical'' coordinates recently proposed by Podolsk\'y and Vr\'atny.
Finally, a pedagogical appendix is thoughtfully included, providing readers
with a user-friendly step-by-step guide to the Ernst formalism, in an attempt
to address and resolve various minor inconsistencies frequently appearing in
the relevant literature.
