During geomagnetic polarity transitions the Earth's internal magnetic field is expected to deviate significantly from the dipolar configuration observed today, and higher-order multipoles can become important. Their effects on the magnetosphere are investigated in this study by means of MHD simulations. We look at quadrupolar configurations and vary the parameters that are expected to be most important in determining the large-scale current systems and the field line topology of such paleomagnetospheres, namely, (1) the orientation of the internal field as well as (2) the orientation of the interplanetary magnetic field (IMF) with respect to the solar wind flow, and (3) the quadrupole shape parameter which controls the topology of the internal field. Zero IMF conditions yield reference cases which allow to locate the magnetopause that otherwise can be obscured by field line merging. Magnetopause currents and cross-tail currents in quadrupolar configurations are contrasted with the tail current system in the present-day dipolar magnetosphere. Interplanetary magnetic fields with a nonzero component perpendicular to the solar wind flow are found to have a much stronger effect on the global magnetospheric configuration than a purely parallel or antiparallel IMF. Since a quadrupole field is more structured than a dipole field, conditions that favor field line merging at the dayside are met regularly in quadrupolar magnetospheres. Solar wind-magnetosphere coupling triggered by reconnection should thus be persistent rather than strongly controlled by solar wind parameters. The investigation presented in this report is part of a multi-institutional collaboration to model the effects of geomagnetic polarity transitions on the Earth's environment in space and the upper and middle atmosphere.