  Pulsating ultra-luminous X-ray sources (PULXs) are characterised by an
extremely large luminosity ($ > 10^{40} \text{erg s}^{-1}$). While there is a
general consensus that they host an accreting, magnetized neutron star (NS),
the problem of how to produce luminosities $> 100$ times the Eddington limit,
$L_E$, of a solar mass object is still debated. A promising explanation relies
on the reduction of the opacities in the presence of a strong magnetic field,
which allows for the local flux to be much larger than the Eddington flux.
However, avoiding the onset of the propeller effect may be a serious problem.
Here, we reconsider the problem of column accretion onto a highly magnetized
NS, extending previously published calculations by relaxing the assumption of a
pure dipolar field and allowing for more complex magnetic field topologies. We
find that the maximum luminosity is determined primarily by the magnetic field
strength near the NS surface. We also investigate other factors determining the
accretion column geometry and the emergent luminosity, such as the assumptions
on the parameters governing the accretion flow at the disk-magnetosphere
boundary. We conclude that a strongly magnetized NS with a dipole component of
$\sim 10^{13} \text{G}$, octupole component of $\sim10^{14} \text{G}$ and spin
period $\sim1 \text{s}$ can produce a luminosity of $\sim 10^{41} \text{erg
s}^{-1}$ while avoiding the propeller regime. We apply our model to two PULXs,
NGC 5907 ULX-1 and NGC 7793 P13, and discuss how their luminosity and spin
period rate can be explained in terms of different configurations, either with
or without multipolar magnetic components.
