  We investigate whether one or many companions are orbiting the extremely
intermittent pulsar PSR B1931+24. We constrained our analysis on previous
observations of eight fundamental properties of PSR B1931+24. The most puzzling
properties are the intermittent nature of the pulsar's activity, with active
and quiet phases that alternate quasi-periodically; the variation of the
slowing-down rate of its period between active and quiet phases; and because
there are no timing residuals, it is highly unlikely that the pulsar has a
massive companion. Here, we examine the effects that one putative companion
immersed in the magnetospheric plasma or the wind of the pulsar might have, as
well as the associated electric current distribution. We analysed several
possibilities for the distance and orbit of this hypothetical companion and the
nature of its interaction with the neutron star. We show that if the
quasi-periodic behaviour of PSR B1931+24 was caused by a companion orbiting the
star with a period of 35 or 70 days, the radio emissions, usually considered to
be those of the pulsar would in that specific case be emitted in the
companion's environment. We analysed four possible configurations and conclude
that none of them would explain the whole set of peculiar properties of PSR
1931+24. We furthermore considered a period 70 days for the precession of the
periastron associated to an orbit very close to the neutron star. This
hypothesis is analysed in a companion paper.
