  Since the detection of X-ray pulses from ultraluminous X-ray sources (ULXs)
in 2014, neutron stars have been considered as their central objects. However,
it remains unclear how neutron stars can be brighter than the Eddington
luminosity, and no unified view exists on the magnetic field of neutron stars
and the degree of beaming. Recent observations suggest that some X-ray
pulsating ULXs have Be-type donors, and some of them occupy the same region as
Be-type high-mass X-ray binaries (Be-HMXBs) on the Corbet diagram, which
reveals the relation between spin and orbital periods. This suggests that at
least some ULXs are special cases of Be-HMXBs. In this study, we use the
framework of mass-accretion models for Be-HMXBs to investigate the conditions
under which neutron stars achieve mass-accretion rates beyond the Eddington
limit and become observable as ULXs. We show that a Be-HMXB may become a ULX if
the magnetic field of the neutron star and the density of the Be disc meet
certain conditions. We also show that, although a stronger magnetic field
increases the brightness of a neutron star ULX with a Be donor, its brightness
cannot exceed the Eddington limit by a more than a factor of ${\approx} 50$.
Finally, we propose a scenario whereby some normal Be-HMXBs may evolve into
ULXs as the donor evolves into a giant.
