  In this paper, we obtain a complete list of stationary and axisymmetric
spacetimes, generated from a Minkowski spacetime using the Ernst technique. We
do so by operating on the associated seed potentials with a composition of
Ehlers and Harrison transformations. In particular, assigning an additional
``electric'' or ``magnetic'' tag to the transformations, we investigate the new
spacetimes obtained either via a composition of magnetic Ehlers and Harrison
transformations (first part) or via a magnetic-electric combination (second
part). In the first part, the resulting type D spacetime, dubbed
electromagnetic swirling universe, features key properties, separately found in
swirling and (Bonnor--)Melvin spacetimes, the latter recovered in appropriate
limits. A detailed analysis of the geometry is included, and subtle issues are
addressed. A detailed proof that the spacetime belongs to the Kundt family, is
included, and a notable relation to the planar-Reissner-Nordstr\"om-NUT black
hole is also meticulously worked out. This relation is further exploited to
reverse-engineer the form of the solution in the presence of a nontrivial
cosmological constant. A Schwarzschild black hole embedded into the new
background is also discussed. In the second part, we present four novel
stationary and axisymmetric asymptotically nonflat type I spacetimes, which are
naively expected to be extensions of the Melvin or swirling solution including
a NUT parameter or electromagnetic charges. We actually find that they are,
under conditions, free of curvature and topological singularities, with the
physical meaning of the electric transformation parameters in these backgrounds
requiring further investigation.
